Subgroups — #46825044

Order 34432.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771356	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771350	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771349	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771344	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771338	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771300	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771298	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771295	C₂	1	1	yes	maximal, characteristic, complemented
9	#31771292	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771286	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771281	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771281	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771255	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771254	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771249	C₂	1	1	yes	maximal, characteristic, complemented
16	#31771223	C₂	1	1	yes	maximal, characteristic, complemented
17	#31771219	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771208	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771205	C₂	1	1	yes	maximal, characteristic, complemented
20	#31771201	C₂	1	1	yes	maximal, characteristic, complemented
21	#31771197	C₂	1	1	yes	maximal, characteristic, complemented
22	#31771193	C₂	1	1	yes	maximal, characteristic, complemented
23	#31771192	C₂	1	1	yes	maximal, characteristic, complemented
24	#31771190	C₂	1	1	yes	maximal, characteristic, complemented
25	#31771188	C₂	1	1	yes	maximal, characteristic, complemented
26	#31771170	C₂	1	1	yes	maximal, characteristic, complemented
27	#31771164	C₂	1	1	yes	maximal, characteristic, complemented
28	#31771113	C₂	1	1	yes	maximal, characteristic, complemented
29	#31771112	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#22575435	C₂	1	1	yes	maximal, characteristic, complemented
31	#546×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#16864401	C₂²	1	1	yes	characteristic
33	C₂×#16864401	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
36	#22575452	C₂²	1	1	yes	characteristic, complemented
37	#22575451	C₂²	1	1	yes	characteristic, complemented
38	#22575449	C₂²	1	1	yes	characteristic
39	#22575449	C₂²	1	1	yes	characteristic, complemented
40	#22575448	C₂²	1	1	yes	characteristic, complemented
41	#22575448	C₂²	1	1	yes	characteristic, complemented
42	#22575448	C₂²	1	1	yes	characteristic, complemented
43	#22575447	C₂²	1	1	yes	characteristic, complemented
44	#22575446	C₂²	1	1	yes	characteristic, complemented
45	#22575446	C₂²	1	1	yes	characteristic, complemented
46	#22575446	C₂²	1	1	yes	characteristic, complemented
47	#22575446	C₂²	1	1	yes	characteristic, complemented
48	#22575446	C₂²	1	1	yes	characteristic, complemented
49	#22575446	C₂²	1	1	yes	characteristic, complemented
50	#22575446	C₂²	1	1	yes	characteristic, complemented
51	#22575446	C₂²	1	1	yes	characteristic, complemented
52	#22575445	C₂²	1	1	yes	characteristic, complemented
53	#22575444	C₂²	1	1	yes	characteristic, complemented
54	#22575443	C₂²	1	1	yes	characteristic, complemented
55	#22575443	C₂²	1	1	yes	characteristic, complemented
56	#22575443	C₂²	1	1	yes	characteristic, complemented
57	#22575443	C₂²	1	1	yes	characteristic, complemented
58	#22575441	C₂²	1	1	yes	characteristic, complemented
59	#22575440	C₂²	1	1	yes	characteristic, complemented
60	#22575440	C₂²	1	1	yes	characteristic, complemented
61	#22575439	C₂²	1	1	yes	characteristic
62	#22575439	C₂²	1	1	yes	characteristic, complemented
63	#22575439	C₂²	1	1	yes	characteristic, complemented
64	#22575439	C₂²	1	1	yes	characteristic, complemented
65	#22575439	C₂²	1	1	yes	characteristic, complemented
66	#22575439	C₂²	1	1	yes	characteristic, complemented
67	#22575438	C₂²	1	1	yes	characteristic, complemented
68	#22575437	C₂²	1	1	yes	characteristic, complemented
69	#22575437	C₂²	1	1	yes	characteristic, complemented
70	#22575437	C₂²	1	1	yes	characteristic, complemented
71	#22575436	C₂²	1	1	yes	characteristic
72	#22575436	C₂²	1	1	yes	characteristic
73	#22575436	C₂²	1	1	yes	characteristic, complemented
74	#22575436	C₂²	1	1	yes	characteristic, complemented
75	#22575436	C₂²	1	1	yes	characteristic, complemented
76	#22575435	C₂²	1	1	yes	characteristic
77	#22575435	C₂²	1	1	yes	characteristic
78	#22575435	C₂²	1	1	yes	characteristic
79	#22575435	C₂²	1	1	yes	characteristic
80	#22575435	C₂²	1	1	yes	characteristic, complemented
81	#22575435	C₂²	1	1	yes	characteristic, complemented
82	#22575435	C₂²	1	1	yes	characteristic, complemented
83	#22575435	C₂²	1	1	yes	characteristic, complemented
84	#22575435	C₂²	1	1	yes	characteristic, complemented
85	#22575435	C₂²	1	1	yes	characteristic, complemented
86	#22575435	C₂²	1	1	yes	characteristic, complemented
87	#22575434	C₂²	1	1	yes	characteristic
88	#22575434	C₂²	1	1	yes	characteristic
89	#22575434	C₂²	1	1	yes	characteristic
90	#22575434	C₂²	1	1	yes	characteristic, complemented
91	#22575434	C₂²	1	1	yes	characteristic, complemented
92	#22575434	C₂²	1	1	yes	characteristic, complemented
93	#22575434	C₂²	1	1	yes	characteristic, complemented
94	#22575434	C₂²	1	1	yes	characteristic, complemented
95	#22575432	C₂²	1	1	yes	characteristic, complemented
96	#22575432	C₂²	1	1	yes	characteristic, complemented
97	#22575432	C₂²	1	1	yes	characteristic, complemented
98	#22575432	C₂²	1	1	yes	characteristic, complemented
99	#22575431	C₂²	1	1	yes	characteristic, complemented
100	#22575431	C₂²	1	1	yes	characteristic, complemented
101	#22575430	C₂²	1	1	yes	characteristic, complemented
102	#22575430	C₂²	1	1	yes	characteristic, complemented
103	#22575430	C₂²	1	1	yes	characteristic, complemented
104	#22575430	C₂²	1	1	yes	characteristic, complemented
105	#22575430	C₂²	1	1	yes	characteristic, complemented
106	#22575430	C₂²	1	1	yes	characteristic, complemented
107	#22575429	C₂²	1	1	yes	characteristic, complemented
108	#22575429	C₂²	1	1	yes	characteristic, complemented
109	#22575429	C₂²	1	1	yes	characteristic, complemented
110	#22575427	C₂²	1	1	yes	characteristic, complemented
111	#22575426	C₂²	1	1	yes	characteristic
112	#22575426	C₂²	1	1	yes	characteristic, complemented
113	#22575426	C₂²	1	1	yes	characteristic, complemented
114	#22575426	C₂²	1	1	yes	characteristic, complemented
115	#22575426	C₂²	1	1	yes	characteristic, complemented
116	#22575425	C₂²	1	1	yes	characteristic
117	#22575425	C₂²	1	1	yes	characteristic
118	#22575425	C₂²	1	1	yes	characteristic
119	#22575425	C₂²	1	1	yes	characteristic
120	#22575425	C₂²	1	1	yes	characteristic
121	#22575425	C₂²	1	1	yes	characteristic
122	#22575425	C₂²	1	1	yes	characteristic, complemented
123	#22575425	C₂²	1	1	yes	characteristic, complemented
124	#22575425	C₂²	1	1	yes	characteristic, complemented
125	#22575425	C₂²	1	1	yes	characteristic, complemented
126	#22575425	C₂²	1	1	yes	characteristic, complemented
127	#22575424	C₂²	1	1	yes	characteristic, complemented
128	#22575424	C₂²	1	1	yes	characteristic, complemented
129	#22575424	C₂²	1	1	yes	characteristic, complemented
130	#22575424	C₂²	1	1	yes	characteristic, complemented
131	#22575423	C₂²	1	1	yes	characteristic, complemented
132	#22575422	C₂²	1	1	yes	characteristic
133	#22575422	C₂²	1	1	yes	characteristic
134	#22575422	C₂²	1	1	yes	characteristic
135	#22575422	C₂²	1	1	yes	characteristic, complemented
136	#22575421	C₂²	1	1	yes	characteristic
137	#22575421	C₂²	1	1	yes	characteristic
138	#22575421	C₂²	1	1	yes	characteristic, complemented
139	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
140	#22575418	C₂²	1	1	yes	characteristic, complemented
141	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
142	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
143	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
144	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
145	#22575415	C₂²	1	1	yes	characteristic, complemented
146	#22575415	C₂²	1	1	yes	characteristic, complemented
147	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
152	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
153	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
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	#22575412	C₂²	1	1	yes	characteristic, complemented
158	#22575412	C₂²	1	1	yes	characteristic, complemented
159	#22575409	C₂²	1	1	yes	characteristic, complemented
160	#22575409	C₂²	1	1	yes	characteristic, complemented
161	#22575409	C₂²	1	1	yes	characteristic, complemented
162	#22575409	C₂²	1	1	yes	characteristic, complemented
163	#22575409	C₂²	1	1	yes	characteristic, complemented
164	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
165	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
166	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
167	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
168	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
169	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
170	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
171	C₂×#16864379	C₂²	1	1	yes	characteristic, complemented
172	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic
173	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
174	#124×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	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
178	#121×C₂₆₉	C₂²	1	1	yes	characteristic
179	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
180	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
181	#120×C₂₆₉	C₂²	1	1	yes	characteristic
182	#120×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
188	#16864401	—	4	2	no	—
189	#16864401	—	4	2	no	—
190	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
191	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
192	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
193	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
194	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
195	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₂₆₉	—	4	2	no	—
197	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₂₆₉	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	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
214	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
215	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
216	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
217	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
218	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
219	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
220	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
221	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₂₆₉	—	4	2	no	—
223	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
240	#16864381	C₂³	1	1	yes	characteristic
241	#16864381	C₂³	1	1	yes	characteristic
242	#16864381	C₂³	1	1	yes	characteristic
243	#16864381	C₂³	1	1	yes	characteristic
244	#16864381	C₂³	1	1	yes	characteristic
245	#16864381	C₂³	1	1	yes	characteristic
246	#16864381	C₂³	1	1	yes	characteristic
247	#16864381	C₂³	1	1	yes	characteristic
248	#16864381	C₂³	1	1	yes	characteristic
249	#16864381	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	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₂₆₉	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	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	#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	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
303	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
304	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
305	C₄×Dic₂₆₉	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	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
312	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
313	#41×C₂₆₉	—	4	2	no	—
314	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₂₆₉	—	4	2	no	—
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	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
320	C₂×D₄×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	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
326	C₂²×C₄×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	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	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
347	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
348	C₂²×D₂₆₉	—	2	2	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	Dic₅₃₈	—	4	1	no	—
355	Dic₅₃₈	—	4	1	no	—
356	Dic₅₃₈	—	4	1	no	—
357	Dic₅₃₈	—	4	1	no	—
358	D₁₀₇₆	—	4	1	no	—
359	D₁₀₇₆	—	4	1	no	—
360	C₂²⋊D₂₆₉	—	2	2	no	—
361	C₂²⋊D₂₆₉	—	4	1	no	—
362	C₂²⋊D₂₆₉	—	4	1	no	—
363	C₂²⋊D₂₆₉	—	4	1	no	—
364	C₂²⋊D₂₆₉	—	4	1	no	—
365	C₂²⋊D₂₆₉	—	4	1	no	—
366	C₂²⋊D₂₆₉	—	4	1	no	—
367	C₂²⋊D₂₆₉	—	4	1	no	—
368	C₂²⋊D₂₆₉	—	4	1	no	—
369	C₂²⋊D₂₆₉	—	4	1	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	C₂×Dic₂₆₉	—	2	2	no	—
377	C₂×Dic₂₆₉	—	2	2	no	—
378	C₂×Dic₂₆₉	—	4	1	no	—
379	C₂×Dic₂₆₉	—	4	1	no	—
380	C₂×Dic₂₆₉	—	4	1	no	—
381	C₂×Dic₂₆₉	—	4	1	no	—
382	C₂×Dic₂₆₉	—	4	1	no	—
383	C₂×Dic₂₆₉	—	4	1	no	—
384	C₂×Dic₂₆₉	—	4	1	no	—
385	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
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	C₄×D₂₆₉	—	4	1	no	—
399	C₄×D₂₆₉	—	4	1	no	—
400	C₄×D₂₆₉	—	4	1	no	—
401	C₄×D₂₆₉	—	4	1	no	—
402	C₄×D₂₆₉	—	4	1	no	—
403	C₄×D₂₆₉	—	4	1	no	—
404	C₄×D₂₆₉	—	4	1	no	—
405	C₂³×C₂₆₉	—	2	2	no	—
406	C₂³×C₂₆₉	—	4	1	no	—
407	C₂³×C₂₆₉	—	4	1	no	—
408	C₂³×C₂₆₉	—	4	1	no	—
409	C₂³×C₂₆₉	—	4	1	no	—
410	C₂³×C₂₆₉	—	4	1	no	—
411	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
412	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
413	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
414	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
415	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
416	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
417	Q₈×C₂₆₉	—	4	1	no	—
418	D₄×C₂₆₉	—	2	2	no	—
419	D₄×C₂₆₉	—	2	2	no	—
420	D₄×C₂₆₉	—	2	2	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	D₄×C₂₆₉	—	4	1	no	—
426	D₄×C₂₆₉	—	4	1	no	—
427	C₂×C₄×C₂₆₉	—	2	2	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	—	4	1	no	—
432	C₂×C₄×C₂₆₉	—	4	1	no	—
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	—	2	1	no	—
455	C₂²×C₂₆₉	—	2	1	no	—
456	C₂²×C₂₆₉	—	2	1	no	—
457	C₂²×C₂₆₉	—	2	1	no	—
458	C₂²×C₂₆₉	—	2	1	no	—
459	C₂²×C₂₆₉	—	8	2	no	—
460	C₂²×C₂₆₉	—	8	2	no	—
461	C₂²×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
462	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
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	—	2	1	no	—
471	C₂×D₂₆₉	—	2	1	no	—
472	C₂×D₂₆₉	—	4	4	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	—	2	1	no	—
493	Dic₂₆₉	—	2	1	no	—
494	Dic₂₆₉	—	2	1	no	—
495	C₂×C₂₆₉	—	2	2	no	—
496	C₂×C₂₆₉	—	4	1	no	—
497	C₂×C₂₆₉	—	4	1	no	—
498	C₂×C₂₆₉	—	4	1	no	—
499	C₂×C₂₆₉	—	4	1	no	—
500	C₂×C₂₆₉	—	4	1	no	—
501	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
502	C₂×C₂₆₉	#585	1	1	yes	characteristic
503	C₂×C₂₆₉	#585	1	1	yes	characteristic
504	D₂₆₉	—	4	1	no	—
505	D₂₆₉	—	4	1	no	—
506	D₂₆₉	—	4	1	no	—
507	C₂₆₉	#3533	1	1	yes	characteristic, complemented, Sylow
508	#3533	—	269	1	no	maximal, Sylow
509	#563	—	269	1	no	—
510	#562	—	269	1	no	—
511	#562	—	269	1	no	—
512	#560	—	269	1	no	—
513	#559	—	269	1	no	—
514	#553	—	269	1	no	—
515	#553	—	269	1	no	—
516	#552	—	269	1	no	—
517	#552	—	269	1	no	—
518	#551	—	269	1	no	—
519	#551	—	269	1	no	—
520	#551	—	269	1	no	—
521	#547	—	269	1	no	—
522	#547	—	269	1	no	—
523	#546	—	269	1	no	—
524	#546	D₂₆₉	1	1	yes	characteristic, complemented
525	#542	—	269	1	no	—
526	#542	—	269	1	no	—
527	#540	—	269	1	no	—
528	#540	—	269	1	no	—
529	#539	—	269	1	no	—
530	#539	—	269	1	no	—
531	#538	—	269	1	no	—
532	#538	—	269	1	no	—
533	#538	—	269	1	no	—
534	#538	—	269	1	no	—
535	#535	—	269	1	no	—
536	#534	—	269	1	no	—
537	#525	—	269	1	no	—
538	#525	—	269	1	no	—
539	C₂×#123	—	269	1	no	—
540	C₂×#41	—	269	1	no	—
541	C₂×#41	—	269	1	no	—
542	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic
543	C₂²×D₄	—	269	1	no	—
544	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic
545	C₂³×C₄	—	269	1	no	—
546	C₄⋊Q₈	—	269	1	no	—
547	C₄⋊Q₈	—	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	—	269	1	no	—
561	#126	—	269	1	no	—
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	#124	—	269	1	no	—
569	#124	—	269	1	no	—
570	#124	—	269	1	no	—
571	#124	—	269	1	no	—
572	#124	—	269	1	no	—
573	#124	—	269	1	no	—
574	#124	—	269	1	no	—
575	#124	—	269	1	no	—
576	#124	—	269	1	no	—
577	#124	C₂×D₂₆₉	1	1	yes	characteristic, complemented
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	—	269	1	no	—
597	#123	—	269	1	no	—
598	#123	—	269	1	no	—
599	#123	—	269	1	no	—
600	#123	—	269	1	no	—
601	#123	—	269	1	no	—
602	#123	—	269	1	no	—
603	#123	—	269	1	no	—
604	#123	—	269	1	no	—
605	#123	—	269	1	no	—
606	#123	C₂×D₂₆₉	1	1	yes	characteristic
607	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
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	C₂×D₂₆₉	1	1	yes	characteristic, complemented
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	C₂×D₂₆₉	1	1	yes	characteristic
646	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
647	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
648	#120	—	269	1	no	—
649	#120	—	269	1	no	—
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	#120	C₂×D₂₆₉	1	1	yes	characteristic
657	#120	C₂×D₂₆₉	1	1	yes	characteristic, complemented
658	C₄×Q₈	—	269	1	no	—
659	C₄×Q₈	—	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, complemented
678	#117	—	269	1	no	—
679	#117	—	269	1	no	—
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	C₂×C₄⋊C₄	—	269	1	no	—
686	C₂×C₄⋊C₄	—	269	1	no	—
687	C₂×C₄⋊C₄	—	269	1	no	—
688	C₂×C₄⋊C₄	—	269	1	no	—
689	C₂×C₂²⋊C₄	—	269	1	no	—
690	C₂×C₂²⋊C₄	—	269	1	no	—
691	C₂×C₂²⋊C₄	—	269	1	no	—
692	C₂×C₂²⋊C₄	—	269	1	no	—
693	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
695	C₂⁴	—	269	1	no	—
696	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
697	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
698	#41	—	4	2	no	—
699	#41	—	1076	2	no	—
700	#41	—	1076	2	no	—
701	C₂×Q₈	—	269	1	no	—
702	C₂×Q₈	—	269	1	no	—
703	C₂×Q₈	—	269	1	no	—
704	C₂×Q₈	—	269	1	no	—
705	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
706	C₂×D₄	—	4	2	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	—	1076	2	no	—
726	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
727	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
728	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
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	—	1076	2	no	—
752	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
753	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
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	C₄⋊C₄	—	269	1	no	—
759	C₄⋊C₄	—	269	1	no	—
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	C₂²⋊C₄	—	269	1	no	—
797	C₂²⋊C₄	—	269	1	no	—
798	C₂²⋊C₄	—	269	1	no	—
799	C₂²⋊C₄	—	269	1	no	—
800	C₂²⋊C₄	—	269	1	no	—
801	C₂²⋊C₄	—	269	1	no	—
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	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
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	—	269	1	no	—
852	C₄²	—	269	1	no	—
853	C₄²	—	269	1	no	—
854	C₄²	—	269	1	no	—
855	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
856	C₂³	—	2	2	no	—
857	C₂³	—	4	1	no	—
858	C₂³	—	4	1	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	1	no	—
861	C₂³	—	4	1	no	—
862	C₂³	—	269	1	no	—
863	C₂³	—	269	1	no	—
864	C₂³	—	269	1	no	—
865	C₂³	—	538	2	no	—
866	C₂³	—	1076	1	no	—
867	C₂³	—	1076	1	no	—
868	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
869	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
870	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
871	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
872	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
873	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
874	Q₈	—	4	1	no	—
875	Q₈	—	1076	1	no	—
876	Q₈	—	1076	1	no	—
877	Q₈	—	1076	1	no	—
878	Q₈	—	1076	1	no	—
879	D₄	—	2	2	no	—
880	D₄	—	2	2	no	—
881	D₄	—	2	2	no	—
882	D₄	—	4	1	no	—
883	D₄	—	4	1	no	—
884	D₄	—	4	1	no	—
885	D₄	—	4	1	no	—
886	D₄	—	4	1	no	—
887	D₄	—	4	1	no	—
888	D₄	—	538	2	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	D₄	—	1076	1	no	—
903	D₄	—	1076	1	no	—
904	D₄	—	1076	1	no	—
905	D₄	—	1076	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	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	—	269	1	no	—
920	C₂×C₄	—	269	1	no	—
921	C₂×C₄	—	269	1	no	—
922	C₂×C₄	—	269	1	no	—
923	C₂×C₄	—	269	1	no	—
924	C₂×C₄	—	269	1	no	—
925	C₂×C₄	—	538	2	no	—
926	C₂×C₄	—	538	2	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	—	1076	1	no	—
938	C₂×C₄	—	1076	1	no	—
939	C₂×C₄	—	1076	1	no	—
940	C₂×C₄	—	1076	1	no	—
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	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
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	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	8	2	no	—
968	C₂²	—	8	2	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	—	538	1	no	—
976	C₂²	—	538	1	no	—
977	C₂²	—	538	1	no	—
978	C₂²	—	1076	4	no	—
979	C₂²	#22575498	1	2	yes	—
980	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
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	—	2	1	no	—
989	C₄	—	2	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	C₄	—	538	1	no	—
1000	C₄	—	538	1	no	—
1001	C₄	—	538	1	no	—
1002	C₄	—	538	1	no	—
1003	C₂	—	2	2	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	4	1	no	—
1008	C₂	—	4	1	no	—
1009	C₂	—	1076	1	no	—
1010	C₂	—	1076	1	no	—
1011	C₂	—	1076	1	no	—
1012	C₂	C₂×#22575498	1	1	yes	characteristic
1013	C₂	#31771440	1	1	yes	characteristic
1014	C₂	#31771441	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#546×C₂₆₉	C₂
hypercenter	#546	D₂₆₉
hypocenter	C₂₆₉	#3533
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #31771356	C₂	semidirect
2. #31771350	C₂	semidirect
3. #31771349	C₂	semidirect
4. #31771344	C₂	semidirect
5. #31771338	C₂	semidirect
6. #31771300	C₂	semidirect
7. #31771298	C₂	semidirect
8. #31771295	C₂	semidirect
9. #31771292	C₂	semidirect
10. #31771286	C₂	semidirect
11. #31771281	C₂	semidirect
12. #31771281	C₂	semidirect
13. #31771255	C₂	semidirect
14. #31771254	C₂	semidirect
15. #31771249	C₂	semidirect
16. #31771223	C₂	semidirect
17. #31771219	C₂	semidirect
18. #31771208	C₂	semidirect
19. #31771205	C₂	semidirect
20. #31771201	C₂	semidirect
21. #31771197	C₂	semidirect
22. #31771193	C₂	semidirect
23. #31771192	C₂	semidirect
24. #31771190	C₂	semidirect
25. #31771188	C₂	semidirect
26. #31771170	C₂	semidirect
27. #31771164	C₂	semidirect
28. #31771113	C₂	semidirect
29. #31771112	C₂	semidirect
30. C₂×#22575435	C₂	semidirect
31. #546×C₂₆₉	C₂	semidirect
33. C₂×#16864401	C₂²	semidirect
35. C₂²×C₄×D₂₆₉	C₂²	semidirect
36. #22575452	C₂²	semidirect
37. #22575451	C₂²	semidirect
39. #22575449	C₂²	semidirect
40. #22575448	C₂²	semidirect
41. #22575448	C₂²	semidirect
42. #22575448	C₂²	semidirect
43. #22575447	C₂²	semidirect
44. #22575446	C₂²	semidirect
45. #22575446	C₂²	semidirect
46. #22575446	C₂²	semidirect
47. #22575446	C₂²	semidirect
48. #22575446	C₂²	semidirect
49. #22575446	C₂²	semidirect
50. #22575446	C₂²	semidirect
51. #22575446	C₂²	semidirect
52. #22575445	C₂²	semidirect
53. #22575444	C₂²	semidirect
54. #22575443	C₂²	semidirect
55. #22575443	C₂²	semidirect
56. #22575443	C₂²	semidirect
57. #22575443	C₂²	semidirect
58. #22575441	C₂²	semidirect
59. #22575440	C₂²	semidirect
60. #22575440	C₂²	semidirect
62. #22575439	C₂²	semidirect
63. #22575439	C₂²	semidirect
64. #22575439	C₂²	semidirect
65. #22575439	C₂²	semidirect
66. #22575439	C₂²	semidirect
67. #22575438	C₂²	semidirect
68. #22575437	C₂²	semidirect
69. #22575437	C₂²	semidirect
70. #22575437	C₂²	semidirect
73. #22575436	C₂²	semidirect
74. #22575436	C₂²	semidirect
75. #22575436	C₂²	semidirect
80. #22575435	C₂²	semidirect
81. #22575435	C₂²	semidirect
82. #22575435	C₂²	semidirect
83. #22575435	C₂²	semidirect
84. #22575435	C₂²	semidirect
85. #22575435	C₂²	semidirect
86. #22575435	C₂²	semidirect
90. #22575434	C₂²	semidirect
91. #22575434	C₂²	semidirect
92. #22575434	C₂²	semidirect
93. #22575434	C₂²	semidirect
94. #22575434	C₂²	semidirect
95. #22575432	C₂²	semidirect
96. #22575432	C₂²	semidirect
97. #22575432	C₂²	semidirect
98. #22575432	C₂²	semidirect
99. #22575431	C₂²	semidirect
100. #22575431	C₂²	semidirect
101. #22575430	C₂²	semidirect
102. #22575430	C₂²	semidirect
103. #22575430	C₂²	semidirect
104. #22575430	C₂²	semidirect
105. #22575430	C₂²	semidirect
106. #22575430	C₂²	semidirect
107. #22575429	C₂²	semidirect
108. #22575429	C₂²	semidirect
109. #22575429	C₂²	semidirect
110. #22575427	C₂²	semidirect
112. #22575426	C₂²	semidirect
113. #22575426	C₂²	semidirect
114. #22575426	C₂²	semidirect
115. #22575426	C₂²	semidirect
122. #22575425	C₂²	semidirect
123. #22575425	C₂²	semidirect
124. #22575425	C₂²	semidirect
125. #22575425	C₂²	semidirect
126. #22575425	C₂²	semidirect
127. #22575424	C₂²	semidirect
128. #22575424	C₂²	semidirect
129. #22575424	C₂²	semidirect
130. #22575424	C₂²	semidirect
131. #22575423	C₂²	semidirect
135. #22575422	C₂²	semidirect
138. #22575421	C₂²	semidirect
139. C₄×Dic₅₃₈	C₂²	semidirect
140. #22575418	C₂²	semidirect
142. D₄×Dic₂₆₉	C₂²	semidirect
143. D₄×Dic₂₆₉	C₂²	semidirect
144. D₄×Dic₂₆₉	C₂²	semidirect
145. #22575415	C₂²	semidirect
146. #22575415	C₂²	semidirect
147. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
148. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
149. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
150. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
151. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
152. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
153. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
154. #22575413	C₂²	semidirect
155. #22575413	C₂²	semidirect
156. #22575413	C₂²	semidirect
157. #22575412	C₂²	semidirect
158. #22575412	C₂²	semidirect
159. #22575409	C₂²	semidirect
160. #22575409	C₂²	semidirect
161. #22575409	C₂²	semidirect
162. #22575409	C₂²	semidirect
163. #22575409	C₂²	semidirect
164. C₂×C₄⋊Dic₂₆₉	C₂²	semidirect
165. C₂×#16864381	C₂²	semidirect
166. C₂×#16864381	C₂²	semidirect
167. C₄⋊C₄×D₂₆₉	C₂²	semidirect
170. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
171. C₂×#16864379	C₂²	semidirect
174. #124×C₂₆₉	C₂²	semidirect
176. #123×C₂₆₉	C₂²	semidirect
177. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
179. #121×C₂₆₉	C₂²	semidirect
180. #121×C₂₆₉	C₂²	semidirect
182. #120×C₂₆₉	C₂²	semidirect
184. C₄×D₄×C₂₆₉	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
507. C₂₆₉	#3533	semidirect
524. #546	D₂₆₉	semidirect
577. #124	C₂×D₂₆₉	semidirect
607. #123	C₂×D₂₆₉	semidirect
623. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
646. #121	C₂×D₂₆₉	semidirect
647. #121	C₂×D₂₆₉	semidirect
657. #120	C₂×D₂₆₉	semidirect
677. C₄×D₄	C₂×D₂₆₉	semidirect
694. C₂×C₂²⋊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
#31771356	2
#31771350	2
#31771349	2
#31771344	2
#31771338	2
#31771300	2
#31771298	2
#31771295	2
#31771292	2
#31771286	2
#31771281	2
#31771255	2
#31771254	2
#31771249	2
#31771223	2
#31771219	2
#31771208	2
#31771205	2
#31771201	2
#31771197	2
#31771193	2
#31771192	2
#31771190	2
#31771188	2
#31771170	2
#31771164	2
#31771113	2
#31771112	2
C₂×#22575435	2
#546×C₂₆₉	2
#3533	269