Subgroups — #46824923

Order 34432.

1124 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771322	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771314	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771309	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771291	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771288	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771281	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771279	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771278	C₂	1	1	yes	maximal, characteristic, complemented
9	#31771268	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771264	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771263	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771253	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771253	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771245	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771242	C₂	1	1	yes	maximal, characteristic, complemented
16	#31771221	C₂	1	1	yes	maximal, characteristic, complemented
17	#31771219	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771204	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771199	C₂	1	1	yes	maximal, characteristic, complemented
20	#31771198	C₂	1	1	yes	maximal, characteristic, complemented
21	#31771196	C₂	1	1	yes	maximal, characteristic, complemented
22	#31771158	C₂	1	1	yes	maximal, characteristic, complemented
23	#31771132	C₂	1	1	yes	maximal, characteristic, complemented
24	#31771114	C₂	1	1	yes	maximal, characteristic, complemented
25	#31771111	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#22575430	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂²⋊Q₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
28	#31771085	C₂	1	1	yes	maximal, characteristic, complemented
29	#31771084	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#22575413	C₂	1	1	yes	maximal, characteristic, complemented
31	#551×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#16864402	C₂²	1	1	yes	characteristic
33	C₂×#16864402	C₂²	1	1	yes	characteristic, complemented
34	C₂×#16864401	C₂²	1	1	yes	characteristic
35	C₂×#16864401	C₂²	1	1	yes	characteristic, complemented
36	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
39	C₂³×Dic₂₆₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
41	#22575452	C₂²	1	1	yes	characteristic, complemented
42	#22575452	C₂²	1	1	yes	characteristic, complemented
43	#22575452	C₂²	1	1	yes	characteristic, complemented
44	#22575451	C₂²	1	1	yes	characteristic, complemented
45	#22575448	C₂²	1	1	yes	characteristic, complemented
46	#22575448	C₂²	1	1	yes	characteristic, complemented
47	#22575448	C₂²	1	1	yes	characteristic, complemented
48	#22575448	C₂²	1	1	yes	characteristic, complemented
49	#22575447	C₂²	1	1	yes	characteristic, complemented
50	#22575446	C₂²	1	1	yes	characteristic, complemented
51	#22575446	C₂²	1	1	yes	characteristic, complemented
52	#22575446	C₂²	1	1	yes	characteristic, complemented
53	#22575445	C₂²	1	1	yes	characteristic, complemented
54	#22575444	C₂²	1	1	yes	characteristic, complemented
55	#22575444	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	#22575441	C₂²	1	1	yes	characteristic, complemented
61	#22575439	C₂²	1	1	yes	characteristic
62	#22575439	C₂²	1	1	yes	characteristic
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	#22575438	C₂²	1	1	yes	characteristic, complemented
67	#22575438	C₂²	1	1	yes	characteristic, complemented
68	#22575438	C₂²	1	1	yes	characteristic, complemented
69	#22575437	C₂²	1	1	yes	characteristic
70	#22575437	C₂²	1	1	yes	characteristic, complemented
71	#22575437	C₂²	1	1	yes	characteristic, complemented
72	#22575437	C₂²	1	1	yes	characteristic, complemented
73	#22575436	C₂²	1	1	yes	characteristic
74	#22575436	C₂²	1	1	yes	characteristic
75	#22575435	C₂²	1	1	yes	characteristic
76	#22575435	C₂²	1	1	yes	characteristic
77	#22575435	C₂²	1	1	yes	characteristic, complemented
78	#22575435	C₂²	1	1	yes	characteristic, complemented
79	#22575435	C₂²	1	1	yes	characteristic, complemented
80	#22575434	C₂²	1	1	yes	characteristic, complemented
81	#22575433	C₂²	1	1	yes	characteristic, complemented
82	#22575433	C₂²	1	1	yes	characteristic, complemented
83	#22575432	C₂²	1	1	yes	characteristic
84	#22575432	C₂²	1	1	yes	characteristic, complemented
85	#22575431	C₂²	1	1	yes	characteristic, complemented
86	#22575431	C₂²	1	1	yes	characteristic, complemented
87	#22575431	C₂²	1	1	yes	characteristic, complemented
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	#22575430	C₂²	1	1	yes	characteristic
92	#22575430	C₂²	1	1	yes	characteristic
93	#22575430	C₂²	1	1	yes	characteristic
94	#22575430	C₂²	1	1	yes	characteristic
95	#22575430	C₂²	1	1	yes	characteristic
96	#22575430	C₂²	1	1	yes	characteristic
97	#22575430	C₂²	1	1	yes	characteristic
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	#22575430	C₂²	1	1	yes	characteristic, complemented
104	#22575430	C₂²	1	1	yes	characteristic, complemented
105	#22575430	C₂²	1	1	yes	characteristic, complemented
106	#22575429	C₂²	1	1	yes	characteristic, complemented
107	#22575429	C₂²	1	1	yes	characteristic, complemented
108	#22575427	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, complemented
112	#22575425	C₂²	1	1	yes	characteristic
113	#22575425	C₂²	1	1	yes	characteristic
114	#22575425	C₂²	1	1	yes	characteristic
115	#22575425	C₂²	1	1	yes	characteristic, complemented
116	#22575424	C₂²	1	1	yes	characteristic
117	#22575423	C₂²	1	1	yes	characteristic
118	#22575422	C₂²	1	1	yes	characteristic
119	#22575421	C₂²	1	1	yes	characteristic
120	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
124	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
125	#22575418	C₂²	1	1	yes	characteristic, complemented
126	#22575418	C₂²	1	1	yes	characteristic, complemented
127	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
129	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
130	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
131	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
132	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
133	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
134	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
135	#22575413	C₂²	1	1	yes	characteristic
136	#22575413	C₂²	1	1	yes	characteristic
137	#22575413	C₂²	1	1	yes	characteristic
138	#22575413	C₂²	1	1	yes	characteristic
139	#22575413	C₂²	1	1	yes	characteristic
140	#22575413	C₂²	1	1	yes	characteristic
141	#22575413	C₂²	1	1	yes	characteristic
142	#22575413	C₂²	1	1	yes	characteristic
143	#22575413	C₂²	1	1	yes	characteristic
144	#22575413	C₂²	1	1	yes	characteristic
145	#22575413	C₂²	1	1	yes	characteristic
146	#22575413	C₂²	1	1	yes	characteristic, complemented
147	#22575413	C₂²	1	1	yes	characteristic, complemented
148	#22575413	C₂²	1	1	yes	characteristic, complemented
149	#22575413	C₂²	1	1	yes	characteristic, complemented
150	#22575412	C₂²	1	1	yes	characteristic
151	#22575411	C₂²	1	1	yes	characteristic, complemented
152	#22575411	C₂²	1	1	yes	characteristic, complemented
153	#22575410	C₂²	1	1	yes	characteristic, complemented
154	#22575410	C₂²	1	1	yes	characteristic, complemented
155	#22575409	C₂²	1	1	yes	characteristic, complemented
156	#22575409	C₂²	1	1	yes	characteristic, complemented
157	#22575409	C₂²	1	1	yes	characteristic, complemented
158	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
159	C₂×#16864381	C₂²	1	1	yes	characteristic
160	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
161	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
162	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
163	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
164	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
165	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
166	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
167	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
168	C₂×#16864379	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
171	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
172	#126×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
173	#126×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
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	#123×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic
179	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
180	#120×C₂₆₉	C₂²	1	1	yes	characteristic
181	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
183	#117×C₂₆₉	C₂²	1	1	yes	characteristic
184	#117×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
187	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
188	#16864402	—	2	4	no	—
189	#16864402	—	4	2	no	—
190	#16864401	—	2	4	no	—
191	#16864401	—	4	2	no	—
192	C₂×Dic₅₃₈	—	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×Dic₅₃₈	C₂³	1	1	yes	characteristic
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	Q₈×D₂₆₉	—	4	2	no	—
202	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
203	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₂₆₉	—	2	4	no	—
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	C₂²×Dic₂₆₉	—	4	2	no	—
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	C₂²×Dic₂₆₉	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	C₂×C₄×D₂₆₉	—	4	2	no	—
228	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₂₆₉	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	C₄⋊Dic₂₆₉	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	#16864381	C₂³	1	1	yes	characteristic
275	#16864381	C₂³	1	1	yes	characteristic
276	#16864381	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	C₂²⋊Dic₂₆₉	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	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	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
312	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
313	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
314	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
315	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
316	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
317	C₂×Q₈×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	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	C₂²×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	C₂²⋊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	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
348	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
349	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
350	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
351	C₂²×D₂₆₉	—	2	2	no	—
352	C₂²×D₂₆₉	—	2	2	no	—
353	C₂²×D₂₆₉	—	4	1	no	—
354	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
355	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
356	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
357	Dic₅₃₈	—	2	2	no	—
358	Dic₅₃₈	—	2	2	no	—
359	Dic₅₃₈	—	2	2	no	—
360	Dic₅₃₈	—	2	2	no	—
361	Dic₅₃₈	—	2	2	no	—
362	Dic₅₃₈	—	4	1	no	—
363	Dic₅₃₈	—	4	1	no	—
364	Dic₅₃₈	—	4	1	no	—
365	D₁₀₇₆	—	2	2	no	—
366	D₁₀₇₆	—	4	1	no	—
367	C₂²⋊D₂₆₉	—	2	2	no	—
368	C₂²⋊D₂₆₉	—	2	2	no	—
369	C₂²⋊D₂₆₉	—	2	2	no	—
370	C₂²⋊D₂₆₉	—	2	2	no	—
371	C₂²⋊D₂₆₉	—	2	2	no	—
372	C₂²⋊D₂₆₉	—	2	2	no	—
373	C₂²⋊D₂₆₉	—	2	2	no	—
374	C₂²⋊D₂₆₉	—	4	1	no	—
375	C₂²⋊D₂₆₉	—	4	1	no	—
376	C₂²⋊D₂₆₉	#41	1	4	yes	complemented
377	C₂×Dic₂₆₉	—	2	2	no	—
378	C₂×Dic₂₆₉	—	2	2	no	—
379	C₂×Dic₂₆₉	—	2	2	no	—
380	C₂×Dic₂₆₉	—	2	2	no	—
381	C₂×Dic₂₆₉	—	2	2	no	—
382	C₂×Dic₂₆₉	—	2	2	no	—
383	C₂×Dic₂₆₉	—	4	1	no	—
384	C₂×Dic₂₆₉	—	4	1	no	—
385	C₂×Dic₂₆₉	—	4	1	no	—
386	C₂×Dic₂₆₉	—	4	1	no	—
387	C₂×Dic₂₆₉	—	4	1	no	—
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	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
401	C₄×D₂₆₉	—	2	2	no	—
402	C₄×D₂₆₉	—	2	2	no	—
403	C₄×D₂₆₉	—	2	2	no	—
404	C₄×D₂₆₉	—	2	2	no	—
405	C₄×D₂₆₉	—	2	2	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	C₂³×C₂₆₉	—	2	2	no	—
413	C₂³×C₂₆₉	—	2	2	no	—
414	C₂³×C₂₆₉	—	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	Q₈×C₂₆₉	—	4	1	no	—
420	D₄×C₂₆₉	—	2	2	no	—
421	D₄×C₂₆₉	—	2	2	no	—
422	D₄×C₂₆₉	—	4	1	no	—
423	C₂×C₄×C₂₆₉	—	2	2	no	—
424	C₂×C₄×C₂₆₉	—	2	2	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	C₂⁴	1	1	yes	characteristic
429	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
430	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
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	C₂²×C₂₆₉	—	2	1	no	—
440	C₂²×C₂₆₉	—	2	1	no	—
441	C₂²×C₂₆₉	—	2	1	no	—
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	—	4	4	no	—
450	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
451	C₂²×C₂₆₉	2₋¹⁺⁴	1	2	yes	—
452	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
453	C₂×D₂₆₉	—	2	1	no	—
454	C₂×D₂₆₉	—	2	1	no	—
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	—	4	4	no	—
462	C₂×D₂₆₉	C₂×#41	1	2	yes	—
463	C₄×C₂₆₉	—	2	1	no	—
464	C₄×C₂₆₉	—	2	1	no	—
465	C₄×C₂₆₉	—	2	1	no	—
466	C₄×C₂₆₉	—	2	1	no	—
467	C₄×C₂₆₉	—	2	1	no	—
468	C₄×C₂₆₉	—	2	1	no	—
469	C₄×C₂₆₉	—	2	1	no	—
470	C₄×C₂₆₉	—	2	1	no	—
471	C₄×C₂₆₉	—	2	1	no	—
472	C₄×C₂₆₉	—	2	1	no	—
473	C₄×C₂₆₉	—	2	1	no	—
474	Dic₂₆₉	—	2	1	no	—
475	Dic₂₆₉	—	2	1	no	—
476	Dic₂₆₉	—	2	1	no	—
477	Dic₂₆₉	—	2	1	no	—
478	Dic₂₆₉	—	2	1	no	—
479	Dic₂₆₉	—	2	1	no	—
480	Dic₂₆₉	—	2	1	no	—
481	Dic₂₆₉	—	2	1	no	—
482	Dic₂₆₉	—	2	1	no	—
483	Dic₂₆₉	—	2	1	no	—
484	Dic₂₆₉	—	2	1	no	—
485	Dic₂₆₉	C₂×#41	1	2	yes	—
486	Dic₂₆₉	H(5,𝔽₂)	1	2	yes	—
487	C₂×C₂₆₉	—	2	2	no	—
488	C₂×C₂₆₉	—	2	2	no	—
489	C₂×C₂₆₉	—	4	1	no	—
490	C₂×C₂₆₉	—	4	1	no	—
491	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
492	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂×C₂₆₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
494	D₂₆₉	—	2	2	no	—
495	D₂₆₉	—	4	1	no	—
496	D₂₆₉	—	4	1	no	—
497	C₂₆₉	#3520	1	1	yes	characteristic, complemented, Sylow
498	#3520	—	269	1	no	maximal, Sylow
499	#556	—	269	1	no	—
500	#554	—	269	1	no	—
501	#554	—	269	1	no	—
502	#552	—	269	1	no	—
503	#552	—	269	1	no	—
504	#551	—	269	1	no	—
505	#551	—	269	1	no	—
506	#551	—	269	1	no	—
507	#551	D₂₆₉	1	1	yes	characteristic, complemented
508	D₄×Q₈	—	269	1	no	—
509	#548	—	269	1	no	—
510	#548	—	269	1	no	—
511	#547	—	269	1	no	—
512	#547	—	269	1	no	—
513	#546	—	269	1	no	—
514	#546	—	269	1	no	—
515	#542	—	269	1	no	—
516	#542	—	269	1	no	—
517	#539	—	269	1	no	—
518	#539	—	269	1	no	—
519	#539	—	269	1	no	—
520	#539	—	269	1	no	—
521	#533	—	269	1	no	—
522	#529	—	269	1	no	—
523	#525	—	269	1	no	—
524	#525	—	269	1	no	—
525	C₂×C₂²⋊Q₈	—	269	1	no	—
526	C₂×C₂²⋊Q₈	—	269	1	no	—
527	#520	—	269	1	no	—
528	#520	—	269	1	no	—
529	C₂×C₄×D₄	—	269	1	no	—
530	C₂×#41	—	269	1	no	—
531	C₂×#41	—	269	1	no	—
532	C₂×#41	—	269	1	no	—
533	C₂×#41	—	269	1	no	—
534	C₂²×Q₈	—	269	1	no	—
535	C₂²×Q₈	—	269	1	no	—
536	C₂²×D₄	—	269	1	no	—
537	C₂³×C₄	—	269	1	no	—
538	C₂³×C₄	—	269	1	no	—
539	C₄⋊Q₈	—	269	1	no	—
540	C₄⋊Q₈	—	269	1	no	—
541	C₄⋊Q₈	—	269	1	no	—
542	C₄⋊Q₈	—	269	1	no	—
543	#126	—	269	1	no	—
544	#126	—	269	1	no	—
545	#126	—	269	1	no	—
546	#126	—	269	1	no	—
547	#126	—	269	1	no	—
548	#126	—	269	1	no	—
549	#126	—	269	1	no	—
550	#126	—	269	1	no	—
551	#126	C₂×D₂₆₉	1	1	yes	characteristic, complemented
552	#126	C₂×D₂₆₉	1	1	yes	characteristic, complemented
553	#125	—	269	1	no	—
554	#125	—	269	1	no	—
555	#125	—	269	1	no	—
556	#125	—	269	1	no	—
557	#125	—	269	1	no	—
558	#125	—	269	1	no	—
559	#125	—	269	1	no	—
560	#124	—	269	1	no	—
561	#124	—	269	1	no	—
562	#124	—	269	1	no	—
563	#124	—	269	1	no	—
564	#124	—	269	1	no	—
565	#124	—	269	1	no	—
566	#124	C₂×D₂₆₉	1	1	yes	characteristic, complemented
567	#123	—	269	1	no	—
568	#123	—	269	1	no	—
569	#123	—	269	1	no	—
570	#123	—	269	1	no	—
571	#123	—	269	1	no	—
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	C₂×D₂₆₉	1	1	yes	characteristic
583	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
584	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
585	C₂²⋊Q₈	—	269	1	no	—
586	C₂²⋊Q₈	—	269	1	no	—
587	C₂²⋊Q₈	—	269	1	no	—
588	C₂²⋊Q₈	—	269	1	no	—
589	C₂²⋊Q₈	—	269	1	no	—
590	C₂²⋊Q₈	—	269	1	no	—
591	C₂²⋊Q₈	—	269	1	no	—
592	C₂²⋊Q₈	—	269	1	no	—
593	C₂²⋊Q₈	—	269	1	no	—
594	C₂²⋊Q₈	—	269	1	no	—
595	C₂²⋊Q₈	—	269	1	no	—
596	C₂²⋊Q₈	—	269	1	no	—
597	C₂²⋊Q₈	—	269	1	no	—
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	C₂²⋊Q₈	—	269	1	no	—
611	C₂²⋊Q₈	—	269	1	no	—
612	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic
613	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
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	#120	—	269	1	no	—
624	#120	—	269	1	no	—
625	#120	—	269	1	no	—
626	#120	C₂×D₂₆₉	1	1	yes	characteristic
627	C₄×Q₈	—	269	1	no	—
628	C₄×Q₈	—	269	1	no	—
629	C₄×Q₈	—	269	1	no	—
630	C₄×Q₈	—	269	1	no	—
631	C₄×Q₈	—	269	1	no	—
632	C₄×Q₈	—	269	1	no	—
633	C₄×Q₈	—	269	1	no	—
634	C₄×D₄	—	269	1	no	—
635	C₄×D₄	—	269	1	no	—
636	C₄×D₄	—	269	1	no	—
637	C₄×D₄	—	269	1	no	—
638	C₄×D₄	—	269	1	no	—
639	C₄×D₄	—	269	1	no	—
640	C₄×D₄	—	269	1	no	—
641	C₄×D₄	—	269	1	no	—
642	C₄×D₄	—	269	1	no	—
643	C₄×D₄	—	269	1	no	—
644	C₄×D₄	—	269	1	no	—
645	C₄×D₄	—	269	1	no	—
646	C₄×D₄	—	269	1	no	—
647	C₄×D₄	—	269	1	no	—
648	C₄×D₄	—	269	1	no	—
649	C₄×D₄	—	269	1	no	—
650	C₄×D₄	—	269	1	no	—
651	C₄×D₄	—	269	1	no	—
652	C₄×D₄	—	269	1	no	—
653	C₄×D₄	—	269	1	no	—
654	C₄×D₄	—	269	1	no	—
655	C₄×D₄	—	269	1	no	—
656	C₄×D₄	—	269	1	no	—
657	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
658	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
659	#117	—	269	1	no	—
660	#117	—	269	1	no	—
661	#117	—	269	1	no	—
662	#117	—	269	1	no	—
663	#117	—	269	1	no	—
664	#117	—	269	1	no	—
665	#117	—	269	1	no	—
666	#117	—	269	1	no	—
667	#117	C₂×D₂₆₉	1	1	yes	characteristic
668	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
669	C₂×C₄⋊C₄	—	269	1	no	—
670	C₂×C₄⋊C₄	—	269	1	no	—
671	C₂×C₄⋊C₄	—	269	1	no	—
672	C₂×C₄⋊C₄	—	269	1	no	—
673	C₂×C₄⋊C₄	—	269	1	no	—
674	C₂×C₄⋊C₄	—	269	1	no	—
675	C₂×C₄⋊C₄	—	269	1	no	—
676	C₂×C₄⋊C₄	—	269	1	no	—
677	C₂×C₄⋊C₄	—	269	1	no	—
678	C₂×C₂²⋊C₄	—	269	1	no	—
679	C₂×C₂²⋊C₄	—	269	1	no	—
680	C₂×C₂²⋊C₄	—	269	1	no	—
681	C₂×C₂²⋊C₄	—	269	1	no	—
682	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic
684	C₂×C₄²	—	269	1	no	—
685	C₂⁴	—	269	1	no	—
686	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
687	#41	—	538	4	no	—
688	#41	—	538	4	no	—
689	#41	—	1076	2	no	—
690	#41	—	1076	2	no	—
691	C₂×Q₈	—	269	1	no	—
692	C₂×Q₈	—	269	1	no	—
693	C₂×Q₈	—	269	1	no	—
694	C₂×Q₈	—	269	1	no	—
695	C₂×Q₈	—	269	1	no	—
696	C₂×Q₈	—	269	1	no	—
697	C₂×Q₈	—	269	1	no	—
698	C₂×Q₈	—	269	1	no	—
699	C₂×Q₈	—	1076	2	no	—
700	C₂×Q₈	—	1076	2	no	—
701	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
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	—	538	4	no	—
715	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
716	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
717	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
718	C₂²×C₄	—	269	1	no	—
719	C₂²×C₄	—	269	1	no	—
720	C₂²×C₄	—	269	1	no	—
721	C₂²×C₄	—	269	1	no	—
722	C₂²×C₄	—	269	1	no	—
723	C₂²×C₄	—	269	1	no	—
724	C₂²×C₄	—	269	1	no	—
725	C₂²×C₄	—	269	1	no	—
726	C₂²×C₄	—	269	1	no	—
727	C₂²×C₄	—	269	1	no	—
728	C₂²×C₄	—	269	1	no	—
729	C₂²×C₄	—	269	1	no	—
730	C₂²×C₄	—	269	1	no	—
731	C₂²×C₄	—	269	1	no	—
732	C₂²×C₄	—	269	1	no	—
733	C₂²×C₄	—	269	1	no	—
734	C₂²×C₄	—	269	1	no	—
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	—	1076	2	no	—
741	C₂²×C₄	—	1076	2	no	—
742	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
743	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
744	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
745	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
746	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
747	C₄⋊C₄	—	269	1	no	—
748	C₄⋊C₄	—	269	1	no	—
749	C₄⋊C₄	—	269	1	no	—
750	C₄⋊C₄	—	269	1	no	—
751	C₄⋊C₄	—	269	1	no	—
752	C₄⋊C₄	—	269	1	no	—
753	C₄⋊C₄	—	269	1	no	—
754	C₄⋊C₄	—	269	1	no	—
755	C₄⋊C₄	—	269	1	no	—
756	C₄⋊C₄	—	269	1	no	—
757	C₄⋊C₄	—	269	1	no	—
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	C₂²×D₂₆₉	1	1	yes	characteristic
786	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
793	C₂²⋊C₄	—	269	1	no	—
794	C₂²⋊C₄	—	269	1	no	—
795	C₂²⋊C₄	—	269	1	no	—
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	C₂²×D₂₆₉	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
829	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
830	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
832	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
834	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
835	C₄²	—	269	1	no	—
836	C₄²	—	269	1	no	—
837	C₄²	—	269	1	no	—
838	C₄²	—	269	1	no	—
839	C₄²	—	269	1	no	—
840	C₄²	—	269	1	no	—
841	C₄²	—	269	1	no	—
842	C₄²	—	269	1	no	—
843	C₄²	—	269	1	no	—
844	C₄²	—	269	1	no	—
845	C₄²	—	269	1	no	—
846	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
847	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
848	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	269	1	no	—
853	C₂³	—	269	1	no	—
854	C₂³	—	269	1	no	—
855	C₂³	—	538	2	no	—
856	C₂³	—	538	2	no	—
857	C₂³	—	1076	1	no	—
858	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
859	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
860	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
861	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
862	Q₈	—	4	1	no	—
863	Q₈	—	538	2	no	—
864	Q₈	—	538	2	no	—
865	Q₈	—	538	2	no	—
866	Q₈	—	538	2	no	—
867	Q₈	—	538	2	no	—
868	Q₈	—	1076	1	no	—
869	Q₈	—	1076	1	no	—
870	Q₈	—	1076	1	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	4	1	no	—
874	D₄	—	269	4	no	—
875	D₄	—	538	2	no	—
876	D₄	—	538	2	no	—
877	D₄	—	538	2	no	—
878	D₄	—	538	2	no	—
879	D₄	—	538	2	no	—
880	D₄	—	538	2	no	—
881	D₄	—	538	2	no	—
882	D₄	—	538	2	no	—
883	D₄	—	1076	1	no	—
884	D₄	—	1076	1	no	—
885	D₄	—	1076	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	269	1	no	—
892	C₂×C₄	—	269	1	no	—
893	C₂×C₄	—	269	1	no	—
894	C₂×C₄	—	269	1	no	—
895	C₂×C₄	—	269	1	no	—
896	C₂×C₄	—	269	1	no	—
897	C₂×C₄	—	269	1	no	—
898	C₂×C₄	—	269	1	no	—
899	C₂×C₄	—	269	1	no	—
900	C₂×C₄	—	269	1	no	—
901	C₂×C₄	—	269	1	no	—
902	C₂×C₄	—	269	1	no	—
903	C₂×C₄	—	269	1	no	—
904	C₂×C₄	—	538	2	no	—
905	C₂×C₄	—	538	2	no	—
906	C₂×C₄	—	538	2	no	—
907	C₂×C₄	—	538	2	no	—
908	C₂×C₄	—	538	2	no	—
909	C₂×C₄	—	538	2	no	—
910	C₂×C₄	—	538	2	no	—
911	C₂×C₄	—	538	2	no	—
912	C₂×C₄	—	538	2	no	—
913	C₂×C₄	—	538	2	no	—
914	C₂×C₄	—	538	2	no	—
915	C₂×C₄	—	1076	1	no	—
916	C₂×C₄	—	1076	1	no	—
917	C₂×C₄	—	1076	1	no	—
918	C₂×C₄	—	1076	1	no	—
919	C₂×C₄	—	1076	1	no	—
920	C₂×C₄	—	1076	1	no	—
921	C₂×C₄	—	1076	1	no	—
922	C₂×C₄	—	1076	1	no	—
923	C₂×C₄	—	1076	1	no	—
924	C₂×C₄	—	1076	1	no	—
925	C₂×C₄	—	1076	1	no	—
926	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
927	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
928	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
929	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
930	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
931	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
932	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
933	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
934	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
935	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
936	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	4	4	no	—
948	C₂²	—	269	2	no	—
949	C₂²	—	538	1	no	—
950	C₂²	—	538	1	no	—
951	C₂²	—	538	1	no	—
952	C₂²	—	538	1	no	—
953	C₂²	—	538	1	no	—
954	C₂²	—	538	1	no	—
955	C₂²	—	538	1	no	—
956	C₂²	—	538	1	no	—
957	C₂²	—	1076	4	no	—
958	C₂²	#41×D₂₆₉	1	2	yes	—
959	C₂²	#22575500	1	2	yes	—
960	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	269	2	no	—
973	C₄	—	269	2	no	—
974	C₄	—	538	1	no	—
975	C₄	—	538	1	no	—
976	C₄	—	538	1	no	—
977	C₄	—	538	1	no	—
978	C₄	—	538	1	no	—
979	C₄	—	538	1	no	—
980	C₄	—	538	1	no	—
981	C₄	—	538	1	no	—
982	C₄	—	538	1	no	—
983	C₄	—	538	1	no	—
984	C₄	—	538	1	no	—
985	C₂	—	2	2	no	—
986	C₂	—	2	2	no	—
987	C₂	—	4	1	no	—
988	C₂	—	4	1	no	—
989	C₂	—	538	2	no	—
990	C₂	—	1076	1	no	—
991	C₂	—	1076	1	no	—
992	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
993	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
994	C₂	C₂×#22575500	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#551×C₂₆₉	C₂
hypercenter	#551	D₂₆₉
hypocenter	C₂₆₉	#3520
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #31771322	C₂	semidirect
2. #31771314	C₂	semidirect
3. #31771309	C₂	semidirect
4. #31771291	C₂	semidirect
5. #31771288	C₂	semidirect
6. #31771281	C₂	semidirect
7. #31771279	C₂	semidirect
8. #31771278	C₂	semidirect
9. #31771268	C₂	semidirect
10. #31771264	C₂	semidirect
11. #31771263	C₂	semidirect
12. #31771253	C₂	semidirect
13. #31771253	C₂	semidirect
14. #31771245	C₂	semidirect
15. #31771242	C₂	semidirect
16. #31771221	C₂	semidirect
17. #31771219	C₂	semidirect
18. #31771204	C₂	semidirect
19. #31771199	C₂	semidirect
20. #31771198	C₂	semidirect
21. #31771196	C₂	semidirect
22. #31771158	C₂	semidirect
23. #31771132	C₂	semidirect
24. #31771114	C₂	semidirect
25. #31771111	C₂	semidirect
26. C₂×#22575430	C₂	semidirect
27. C₂²⋊Q₈×D₂₆₉	C₂	semidirect
28. #31771085	C₂	semidirect
29. #31771084	C₂	semidirect
30. C₂×#22575413	C₂	semidirect
31. #551×C₂₆₉	C₂	semidirect
33. C₂×#16864402	C₂²	semidirect
35. C₂×#16864401	C₂²	semidirect
36. C₂²×Dic₅₃₈	C₂²	semidirect
37. C₂×Q₈×D₂₆₉	C₂²	semidirect
41. #22575452	C₂²	semidirect
42. #22575452	C₂²	semidirect
43. #22575452	C₂²	semidirect
44. #22575451	C₂²	semidirect
45. #22575448	C₂²	semidirect
46. #22575448	C₂²	semidirect
47. #22575448	C₂²	semidirect
48. #22575448	C₂²	semidirect
49. #22575447	C₂²	semidirect
50. #22575446	C₂²	semidirect
51. #22575446	C₂²	semidirect
52. #22575446	C₂²	semidirect
53. #22575445	C₂²	semidirect
54. #22575444	C₂²	semidirect
55. #22575444	C₂²	semidirect
56. #22575444	C₂²	semidirect
57. #22575443	C₂²	semidirect
58. #22575443	C₂²	semidirect
59. #22575443	C₂²	semidirect
60. #22575441	C₂²	semidirect
63. #22575439	C₂²	semidirect
64. #22575439	C₂²	semidirect
65. #22575439	C₂²	semidirect
66. #22575438	C₂²	semidirect
67. #22575438	C₂²	semidirect
68. #22575438	C₂²	semidirect
70. #22575437	C₂²	semidirect
71. #22575437	C₂²	semidirect
72. #22575437	C₂²	semidirect
77. #22575435	C₂²	semidirect
78. #22575435	C₂²	semidirect
79. #22575435	C₂²	semidirect
80. #22575434	C₂²	semidirect
81. #22575433	C₂²	semidirect
82. #22575433	C₂²	semidirect
84. #22575432	C₂²	semidirect
85. #22575431	C₂²	semidirect
86. #22575431	C₂²	semidirect
87. #22575431	C₂²	semidirect
88. #22575431	C₂²	semidirect
89. #22575431	C₂²	semidirect
90. #22575431	C₂²	semidirect
98. #22575430	C₂²	semidirect
99. #22575430	C₂²	semidirect
100. #22575430	C₂²	semidirect
101. #22575430	C₂²	semidirect
102. #22575430	C₂²	semidirect
103. #22575430	C₂²	semidirect
104. #22575430	C₂²	semidirect
105. #22575430	C₂²	semidirect
106. #22575429	C₂²	semidirect
107. #22575429	C₂²	semidirect
111. #22575426	C₂²	semidirect
115. #22575425	C₂²	semidirect
120. C₄×Dic₅₃₈	C₂²	semidirect
121. C₄×Dic₅₃₈	C₂²	semidirect
122. C₄×Dic₅₃₈	C₂²	semidirect
123. C₄×Dic₅₃₈	C₂²	semidirect
124. C₄×Dic₅₃₈	C₂²	semidirect
125. #22575418	C₂²	semidirect
126. #22575418	C₂²	semidirect
127. C₄×D₁₀₇₆	C₂²	semidirect
128. C₄×D₁₀₇₆	C₂²	semidirect
131. D₄×Dic₂₆₉	C₂²	semidirect
134. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
146. #22575413	C₂²	semidirect
147. #22575413	C₂²	semidirect
148. #22575413	C₂²	semidirect
149. #22575413	C₂²	semidirect
151. #22575411	C₂²	semidirect
152. #22575411	C₂²	semidirect
153. #22575410	C₂²	semidirect
154. #22575410	C₂²	semidirect
155. #22575409	C₂²	semidirect
156. #22575409	C₂²	semidirect
157. #22575409	C₂²	semidirect
158. C₂×C₄⋊Dic₂₆₉	C₂²	semidirect
160. C₂×#16864381	C₂²	semidirect
161. C₂×#16864381	C₂²	semidirect
162. C₂×#16864381	C₂²	semidirect
163. C₄⋊C₄×D₂₆₉	C₂²	semidirect
164. C₄⋊C₄×D₂₆₉	C₂²	semidirect
165. C₄⋊C₄×D₂₆₉	C₂²	semidirect
166. C₄⋊C₄×D₂₆₉	C₂²	semidirect
172. #126×C₂₆₉	C₂²	semidirect
173. #126×C₂₆₉	C₂²	semidirect
174. #124×C₂₆₉	C₂²	semidirect
176. #123×C₂₆₉	C₂²	semidirect
177. #123×C₂₆₉	C₂²	semidirect
179. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
182. C₄×D₄×C₂₆₉	C₂²	semidirect
184. #117×C₂₆₉	C₂²	semidirect
376. C₂²⋊D₂₆₉	#41	semidirect
497. C₂₆₉	#3520	semidirect
507. #551	D₂₆₉	semidirect
551. #126	C₂×D₂₆₉	semidirect
552. #126	C₂×D₂₆₉	semidirect
566. #124	C₂×D₂₆₉	semidirect
583. #123	C₂×D₂₆₉	semidirect
584. #123	C₂×D₂₆₉	semidirect
613. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
658. C₄×D₄	C₂×D₂₆₉	semidirect
668. #117	C₂×D₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
#31771322	2
#31771314	2
#31771309	2
#31771291	2
#31771288	2
#31771281	2
#31771279	2
#31771278	2
#31771268	2
#31771264	2
#31771263	2
#31771253	2
#31771245	2
#31771242	2
#31771221	2
#31771219	2
#31771204	2
#31771199	2
#31771198	2
#31771196	2
#31771158	2
#31771132	2
#31771114	2
#31771111	2
C₂×#22575430	2
C₂²⋊Q₈×D₂₆₉	2
#31771085	2
#31771084	2
C₂×#22575413	2
#551×C₂₆₉	2
#3520	269