Subgroups — #46825175

Order 34432.

1032 conjugacy classes of subgroups.

The subgroup lattice has 980 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	#31771352	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771351	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771322	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771316	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771311	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771309	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771308	C₂	1	1	yes	maximal, characteristic, complemented
9	#31771306	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771306	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771291	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771270	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771265	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771263	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771253	C₂	1	1	yes	maximal, characteristic, complemented
16	#31771229	C₂	1	1	yes	maximal, characteristic, complemented
17	#31771221	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771221	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771214	C₂	1	1	yes	maximal, characteristic, complemented
20	#31771204	C₂	1	1	yes	maximal, characteristic, complemented
21	#31771203	C₂	1	1	yes	maximal, characteristic, complemented
22	#31771194	C₂	1	1	yes	maximal, characteristic, complemented
23	#31771194	C₂	1	1	yes	maximal, characteristic, complemented
24	#31771191	C₂	1	1	yes	maximal, characteristic, complemented
25	#31771189	C₂	1	1	yes	maximal, characteristic, complemented
26	#31771185	C₂	1	1	yes	maximal, characteristic, complemented
27	#31771180	C₂	1	1	yes	maximal, characteristic, complemented
28	#31771118	C₂	1	1	yes	maximal, characteristic, complemented
29	#31771113	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂²⋊Q₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
31	#563×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#16864403	C₂²	1	1	yes	characteristic
33	C₂×#16864402	C₂²	1	1	yes	characteristic, complemented
34	C₂×#16864401	C₂²	1	1	yes	characteristic
35	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic
36	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
38	#22575452	C₂²	1	1	yes	characteristic, complemented
39	#22575452	C₂²	1	1	yes	characteristic, complemented
40	#22575452	C₂²	1	1	yes	characteristic, complemented
41	#22575451	C₂²	1	1	yes	characteristic, complemented
42	#22575448	C₂²	1	1	yes	characteristic
43	#22575448	C₂²	1	1	yes	characteristic
44	#22575448	C₂²	1	1	yes	characteristic
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
50	#22575446	C₂²	1	1	yes	characteristic
51	#22575446	C₂²	1	1	yes	characteristic
52	#22575444	C₂²	1	1	yes	characteristic, complemented
53	#22575444	C₂²	1	1	yes	characteristic, complemented
54	#22575444	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	#22575443	C₂²	1	1	yes	characteristic, complemented
59	#22575442	C₂²	1	1	yes	characteristic
60	#22575442	C₂²	1	1	yes	characteristic, complemented
61	#22575441	C₂²	1	1	yes	characteristic
62	#22575441	C₂²	1	1	yes	characteristic
63	#22575439	C₂²	1	1	yes	characteristic
64	#22575439	C₂²	1	1	yes	characteristic
65	#22575439	C₂²	1	1	yes	characteristic
66	#22575439	C₂²	1	1	yes	characteristic
67	#22575439	C₂²	1	1	yes	characteristic, complemented
68	#22575439	C₂²	1	1	yes	characteristic, complemented
69	#22575438	C₂²	1	1	yes	characteristic
70	#22575438	C₂²	1	1	yes	characteristic
71	#22575438	C₂²	1	1	yes	characteristic
72	#22575438	C₂²	1	1	yes	characteristic
73	#22575438	C₂²	1	1	yes	characteristic
74	#22575438	C₂²	1	1	yes	characteristic, complemented
75	#22575438	C₂²	1	1	yes	characteristic, complemented
76	#22575438	C₂²	1	1	yes	characteristic, complemented
77	#22575438	C₂²	1	1	yes	characteristic, complemented
78	#22575437	C₂²	1	1	yes	characteristic
79	#22575437	C₂²	1	1	yes	characteristic, complemented
80	#22575437	C₂²	1	1	yes	characteristic, complemented
81	#22575436	C₂²	1	1	yes	characteristic
82	#22575435	C₂²	1	1	yes	characteristic
83	#22575435	C₂²	1	1	yes	characteristic
84	#22575435	C₂²	1	1	yes	characteristic
85	#22575433	C₂²	1	1	yes	characteristic
86	#22575433	C₂²	1	1	yes	characteristic
87	#22575433	C₂²	1	1	yes	characteristic, complemented
88	#22575433	C₂²	1	1	yes	characteristic, complemented
89	#22575432	C₂²	1	1	yes	characteristic
90	#22575431	C₂²	1	1	yes	characteristic
91	#22575431	C₂²	1	1	yes	characteristic
92	#22575431	C₂²	1	1	yes	characteristic
93	#22575431	C₂²	1	1	yes	characteristic
94	#22575431	C₂²	1	1	yes	characteristic
95	#22575431	C₂²	1	1	yes	characteristic
96	#22575431	C₂²	1	1	yes	characteristic, complemented
97	#22575431	C₂²	1	1	yes	characteristic, complemented
98	#22575431	C₂²	1	1	yes	characteristic, complemented
99	#22575431	C₂²	1	1	yes	characteristic, complemented
100	#22575431	C₂²	1	1	yes	characteristic, complemented
101	#22575431	C₂²	1	1	yes	characteristic, complemented
102	#22575430	C₂²	1	1	yes	characteristic
103	#22575430	C₂²	1	1	yes	characteristic
104	#22575430	C₂²	1	1	yes	characteristic, complemented
105	#22575430	C₂²	1	1	yes	characteristic, complemented
106	#22575429	C₂²	1	1	yes	characteristic
107	#22575429	C₂²	1	1	yes	characteristic
108	#22575429	C₂²	1	1	yes	characteristic
109	#22575429	C₂²	1	1	yes	characteristic, complemented
110	#22575429	C₂²	1	1	yes	characteristic, complemented
111	#22575429	C₂²	1	1	yes	characteristic, complemented
112	#22575428	C₂²	1	1	yes	characteristic
113	#22575428	C₂²	1	1	yes	characteristic
114	#22575428	C₂²	1	1	yes	characteristic
115	#22575428	C₂²	1	1	yes	characteristic
116	#22575428	C₂²	1	1	yes	characteristic
117	#22575428	C₂²	1	1	yes	characteristic, complemented
118	#22575427	C₂²	1	1	yes	characteristic
119	#22575427	C₂²	1	1	yes	characteristic
120	#22575426	C₂²	1	1	yes	characteristic
121	#22575426	C₂²	1	1	yes	characteristic
122	#22575426	C₂²	1	1	yes	characteristic
123	#22575426	C₂²	1	1	yes	characteristic
124	#22575426	C₂²	1	1	yes	characteristic
125	#22575426	C₂²	1	1	yes	characteristic
126	#22575426	C₂²	1	1	yes	characteristic
127	#22575426	C₂²	1	1	yes	characteristic, complemented
128	#22575426	C₂²	1	1	yes	characteristic, complemented
129	#22575425	C₂²	1	1	yes	characteristic
130	#22575424	C₂²	1	1	yes	characteristic
131	#22575423	C₂²	1	1	yes	characteristic
132	#22575423	C₂²	1	1	yes	characteristic
133	#22575423	C₂²	1	1	yes	characteristic
134	#22575421	C₂²	1	1	yes	characteristic
135	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
136	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
137	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
138	#22575418	C₂²	1	1	yes	characteristic, complemented
139	#22575418	C₂²	1	1	yes	characteristic, complemented
140	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
141	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
142	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
143	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
144	#22575415	C₂²	1	1	yes	characteristic
145	#22575415	C₂²	1	1	yes	characteristic
146	#22575415	C₂²	1	1	yes	characteristic
147	#22575415	C₂²	1	1	yes	characteristic
148	#22575415	C₂²	1	1	yes	characteristic
149	#22575415	C₂²	1	1	yes	characteristic
150	#22575415	C₂²	1	1	yes	characteristic
151	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
152	#22575413	C₂²	1	1	yes	characteristic
153	#22575413	C₂²	1	1	yes	characteristic
154	#22575413	C₂²	1	1	yes	characteristic
155	#22575413	C₂²	1	1	yes	characteristic
156	#22575413	C₂²	1	1	yes	characteristic
157	#22575413	C₂²	1	1	yes	characteristic, complemented
158	#22575413	C₂²	1	1	yes	characteristic, complemented
159	#22575411	C₂²	1	1	yes	characteristic
160	#22575411	C₂²	1	1	yes	characteristic, complemented
161	#22575410	C₂²	1	1	yes	characteristic, complemented
162	#22575410	C₂²	1	1	yes	characteristic, complemented
163	#22575409	C₂²	1	1	yes	characteristic
164	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
165	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
166	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
167	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
168	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
169	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
172	C₄⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
173	C₄⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
174	#126×C₂₆₉	C₂²	1	1	yes	characteristic
175	#126×C₂₆₉	C₂²	1	1	yes	characteristic
176	#126×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
177	#126×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
178	#125×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
179	#125×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
180	#124×C₂₆₉	C₂²	1	1	yes	characteristic
181	#123×C₂₆₉	C₂²	1	1	yes	characteristic
182	#123×C₂₆₉	C₂²	1	1	yes	characteristic
183	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic
184	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic
185	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
186	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
188	#16864403	—	4	2	no	—
189	#16864402	—	4	2	no	—
190	#16864401	—	4	2	no	—
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×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	Q₈×D₂₆₉	—	4	2	no	—
199	Q₈×D₂₆₉	—	4	2	no	—
200	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
201	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
202	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
203	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
204	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
205	C₂×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×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
217	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
218	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
219	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₂₆₉	—	4	2	no	—
221	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
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	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	C₄⋊Dic₂₆₉	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	#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	#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	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	#16864379	C₂³	1	1	yes	characteristic
275	#16864379	C₂³	1	1	yes	characteristic
276	#16864379	C₂³	1	1	yes	characteristic
277	#16864379	C₂³	1	1	yes	characteristic
278	#16864379	C₂³	1	1	yes	characteristic
279	#16864379	C₂³	1	1	yes	characteristic
280	#16864379	C₂³	1	1	yes	characteristic
281	#16864379	C₂³	1	1	yes	characteristic
282	#16864379	C₂³	1	1	yes	characteristic
283	#16864379	C₂³	1	1	yes	characteristic
284	#16864379	C₂³	1	1	yes	characteristic
285	#16864379	C₂³	1	1	yes	characteristic
286	#16864379	C₂³	1	1	yes	characteristic
287	#16864379	C₂³	1	1	yes	characteristic
288	#16864379	C₂³	1	1	yes	characteristic
289	#16864379	C₂³	1	1	yes	characteristic
290	#16864379	C₂³	1	1	yes	characteristic
291	#16864379	C₂³	1	1	yes	characteristic
292	#16864379	C₂³	1	1	yes	characteristic
293	#16864379	C₂³	1	1	yes	characteristic
294	#16864379	C₂³	1	1	yes	characteristic
295	#16864379	C₂³	1	1	yes	characteristic
296	#16864379	C₂³	1	1	yes	characteristic
297	#16864379	C₂³	1	1	yes	characteristic
298	#16864379	C₂³	1	1	yes	characteristic
299	#16864379	C₂³	1	1	yes	characteristic
300	#16864379	C₂³	1	1	yes	characteristic
301	#16864379	C₂³	1	1	yes	characteristic
302	#16864379	C₂³	1	1	yes	characteristic
303	#16864379	C₂³	1	1	yes	characteristic
304	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	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
312	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
313	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
314	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
315	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
317	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
318	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
345	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
346	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
347	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
348	C₂²×D₂₆₉	—	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	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
355	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
356	Dic₅₃₈	—	2	2	no	—
357	Dic₅₃₈	—	2	2	no	—
358	Dic₅₃₈	—	2	2	no	—
359	Dic₅₃₈	—	4	1	no	—
360	Dic₅₃₈	—	4	1	no	—
361	Dic₅₃₈	—	4	1	no	—
362	Dic₅₃₈	—	4	1	no	—
363	D₁₀₇₆	—	2	2	no	—
364	D₁₀₇₆	—	2	2	no	—
365	D₁₀₇₆	—	2	2	no	—
366	D₁₀₇₆	—	4	1	no	—
367	D₁₀₇₆	—	4	1	no	—
368	D₁₀₇₆	—	4	1	no	—
369	D₁₀₇₆	—	4	1	no	—
370	D₁₀₇₆	—	4	1	no	—
371	D₁₀₇₆	—	4	1	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	—	4	1	no	—
377	C₂²⋊D₂₆₉	—	4	1	no	—
378	C₂²⋊D₂₆₉	—	4	1	no	—
379	C₂²⋊D₂₆₉	—	4	1	no	—
380	C₂×Dic₂₆₉	—	2	2	no	—
381	C₂×Dic₂₆₉	—	4	1	no	—
382	C₂×Dic₂₆₉	—	4	1	no	—
383	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
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	C₄×D₂₆₉	—	2	2	no	—
395	C₄×D₂₆₉	—	2	2	no	—
396	C₄×D₂₆₉	—	2	2	no	—
397	C₄×D₂₆₉	—	2	2	no	—
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	C₄×D₂₆₉	—	4	1	no	—
406	C₄×D₂₆₉	—	4	1	no	—
407	C₄×D₂₆₉	—	4	1	no	—
408	C₄×D₂₆₉	—	4	1	no	—
409	C₄×D₂₆₉	—	4	1	no	—
410	C₄×D₂₆₉	—	4	1	no	—
411	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
412	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
413	Q₈×C₂₆₉	—	4	1	no	—
414	Q₈×C₂₆₉	—	4	1	no	—
415	Q₈×C₂₆₉	—	4	1	no	—
416	D₄×C₂₆₉	—	4	1	no	—
417	C₂×C₄×C₂₆₉	—	4	1	no	—
418	C₂×C₄×C₂₆₉	—	4	1	no	—
419	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
420	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
421	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
423	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
424	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
425	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
426	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
427	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
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	C₂²×C₂₆₉	—	2	1	no	—
433	C₂²×C₂₆₉	—	2	1	no	—
434	C₂²×C₂₆₉	—	2	1	no	—
435	C₂²×C₂₆₉	—	2	1	no	—
436	C₂²×C₂₆₉	—	2	1	no	—
437	C₂²×C₂₆₉	—	2	1	no	—
438	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
439	C₂×D₂₆₉	—	2	1	no	—
440	C₂×D₂₆₉	—	2	1	no	—
441	C₂×D₂₆₉	—	2	1	no	—
442	C₂×D₂₆₉	—	2	1	no	—
443	C₂×D₂₆₉	—	2	1	no	—
444	C₂×D₂₆₉	—	2	1	no	—
445	C₂×D₂₆₉	—	2	1	no	—
446	C₂×D₂₆₉	—	2	1	no	—
447	C₂×D₂₆₉	—	2	1	no	—
448	C₂×D₂₆₉	—	2	1	no	—
449	C₂×D₂₆₉	—	2	1	no	—
450	C₂×D₂₆₉	—	2	1	no	—
451	C₂×D₂₆₉	—	2	1	no	—
452	C₂×D₂₆₉	—	2	1	no	—
453	C₂×D₂₆₉	—	4	4	no	—
454	C₂×D₂₆₉	2₋¹⁺⁴	1	2	yes	—
455	C₄×C₂₆₉	—	2	1	no	—
456	C₄×C₂₆₉	—	2	1	no	—
457	C₄×C₂₆₉	—	2	1	no	—
458	C₄×C₂₆₉	—	2	1	no	—
459	C₄×C₂₆₉	—	2	1	no	—
460	C₄×C₂₆₉	—	2	1	no	—
461	C₄×C₂₆₉	—	2	1	no	—
462	C₄×C₂₆₉	—	2	1	no	—
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	Dic₂₆₉	—	2	1	no	—
469	Dic₂₆₉	—	2	1	no	—
470	Dic₂₆₉	—	2	1	no	—
471	Dic₂₆₉	—	2	1	no	—
472	Dic₂₆₉	—	2	1	no	—
473	Dic₂₆₉	—	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	H(5,𝔽₂)	1	2	yes	—
479	C₂×C₂₆₉	—	4	1	no	—
480	C₂×C₂₆₉	—	4	1	no	—
481	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂×C₂₆₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂×C₂₆₉	#585	1	1	yes	characteristic
484	D₂₆₉	—	2	2	no	—
485	D₂₆₉	—	4	1	no	—
486	D₂₆₉	—	4	1	no	—
487	D₂₆₉	—	4	1	no	—
488	D₂₆₉	—	4	1	no	—
489	C₂₆₉	#3541	1	1	yes	characteristic, complemented, Sylow
490	#3541	—	269	1	no	maximal, Sylow
491	#563	—	269	1	no	—
492	#563	D₂₆₉	1	1	yes	characteristic, complemented
493	#562	—	269	1	no	—
494	#562	—	269	1	no	—
495	#556	—	269	1	no	—
496	#554	—	269	1	no	—
497	#554	—	269	1	no	—
498	#554	—	269	1	no	—
499	#553	—	269	1	no	—
500	#553	—	269	1	no	—
501	#553	—	269	1	no	—
502	#552	—	269	1	no	—
503	D₄×Q₈	—	269	1	no	—
504	#548	—	269	1	no	—
505	#548	—	269	1	no	—
506	#547	—	269	1	no	—
507	#542	—	269	1	no	—
508	#542	—	269	1	no	—
509	#542	—	269	1	no	—
510	#541	—	269	1	no	—
511	#539	—	269	1	no	—
512	#539	—	269	1	no	—
513	#538	—	269	1	no	—
514	#538	—	269	1	no	—
515	#538	—	269	1	no	—
516	#538	—	269	1	no	—
517	#537	—	269	1	no	—
518	#536	—	269	1	no	—
519	#525	—	269	1	no	—
520	#525	—	269	1	no	—
521	C₂×C₂²⋊Q₈	—	269	1	no	—
522	C₂×#41	—	269	1	no	—
523	C₂×#41	—	269	1	no	—
524	C₂×#41	—	269	1	no	—
525	C₂²×Q₈	—	269	1	no	—
526	C₂²×Q₈	—	269	1	no	—
527	C₂³×C₄	—	269	1	no	—
528	C₄⋊Q₈	—	269	1	no	—
529	C₄⋊Q₈	—	269	1	no	—
530	C₄⋊Q₈	—	269	1	no	—
531	C₄⋊Q₈	—	269	1	no	—
532	C₄⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
533	C₄⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
534	#126	—	269	1	no	—
535	#126	—	269	1	no	—
536	#126	—	269	1	no	—
537	#126	—	269	1	no	—
538	#126	—	269	1	no	—
539	#126	—	269	1	no	—
540	#126	—	269	1	no	—
541	#126	—	269	1	no	—
542	#126	—	269	1	no	—
543	#126	—	269	1	no	—
544	#126	C₂×D₂₆₉	1	1	yes	characteristic
545	#126	C₂×D₂₆₉	1	1	yes	characteristic
546	#126	C₂×D₂₆₉	1	1	yes	characteristic, complemented
547	#126	C₂×D₂₆₉	1	1	yes	characteristic, complemented
548	#125	—	269	1	no	—
549	#125	—	269	1	no	—
550	#125	—	269	1	no	—
551	#125	—	269	1	no	—
552	#125	—	269	1	no	—
553	#125	—	269	1	no	—
554	#125	—	269	1	no	—
555	#125	C₂×D₂₆₉	1	1	yes	characteristic, complemented
556	#125	C₂×D₂₆₉	1	1	yes	characteristic, complemented
557	#124	—	269	1	no	—
558	#124	—	269	1	no	—
559	#124	—	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	—	269	1	no	—
567	#124	C₂×D₂₆₉	1	1	yes	characteristic
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	—	269	1	no	—
583	#123	—	269	1	no	—
584	#123	C₂×D₂₆₉	1	1	yes	characteristic
585	#123	C₂×D₂₆₉	1	1	yes	characteristic
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	—	269	1	no	—
613	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic
614	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic
615	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
616	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
617	#121	—	269	1	no	—
618	#121	—	269	1	no	—
619	#121	—	269	1	no	—
620	#121	—	269	1	no	—
621	#121	—	269	1	no	—
622	#121	—	269	1	no	—
623	#121	—	269	1	no	—
624	#121	—	269	1	no	—
625	#121	—	269	1	no	—
626	#121	—	269	1	no	—
627	#121	—	269	1	no	—
628	#121	—	269	1	no	—
629	#121	—	269	1	no	—
630	#121	—	269	1	no	—
631	#121	—	269	1	no	—
632	#121	—	269	1	no	—
633	#121	—	269	1	no	—
634	#121	—	269	1	no	—
635	#121	—	269	1	no	—
636	#120	—	269	1	no	—
637	#120	—	269	1	no	—
638	#120	—	269	1	no	—
639	#120	—	269	1	no	—
640	C₄×Q₈	—	269	1	no	—
641	C₄×Q₈	—	269	1	no	—
642	C₄×Q₈	—	269	1	no	—
643	C₄×Q₈	—	269	1	no	—
644	C₄×Q₈	—	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	—	269	1	no	—
658	C₄×D₄	—	269	1	no	—
659	C₄×D₄	—	269	1	no	—
660	C₄×D₄	—	269	1	no	—
661	C₄×D₄	—	269	1	no	—
662	C₄×D₄	—	269	1	no	—
663	C₄×D₄	—	269	1	no	—
664	#117	—	269	1	no	—
665	#117	—	269	1	no	—
666	#117	—	269	1	no	—
667	#117	—	269	1	no	—
668	#117	—	269	1	no	—
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×C₂²⋊C₄	—	269	1	no	—
676	C₂×C₂²⋊C₄	—	269	1	no	—
677	C₂⁴	—	269	1	no	—
678	#41	—	1076	2	no	—
679	#41	—	1076	2	no	—
680	#41	—	1076	2	no	—
681	C₂×Q₈	—	269	1	no	—
682	C₂×Q₈	—	269	1	no	—
683	C₂×Q₈	—	269	1	no	—
684	C₂×Q₈	—	269	1	no	—
685	C₂×Q₈	—	269	1	no	—
686	C₂×Q₈	—	269	1	no	—
687	C₂×Q₈	—	269	1	no	—
688	C₂×Q₈	—	1076	2	no	—
689	C₂×Q₈	—	1076	2	no	—
690	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
691	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
692	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
693	C₂×D₄	—	269	1	no	—
694	C₂×D₄	—	269	1	no	—
695	C₂×D₄	—	269	1	no	—
696	C₂×D₄	—	269	1	no	—
697	C₂×D₄	—	269	1	no	—
698	C₂×D₄	—	269	1	no	—
699	C₂×D₄	—	269	1	no	—
700	C₂×D₄	—	269	1	no	—
701	C₂×D₄	—	269	1	no	—
702	C₂×D₄	—	269	1	no	—
703	C₂×D₄	—	269	1	no	—
704	C₂×D₄	—	269	1	no	—
705	C₂×D₄	—	269	1	no	—
706	C₂×D₄	—	269	1	no	—
707	C₂×D₄	—	269	1	no	—
708	C₂×D₄	—	269	1	no	—
709	C₂×D₄	—	269	1	no	—
710	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
711	C₂²×C₄	—	269	1	no	—
712	C₂²×C₄	—	269	1	no	—
713	C₂²×C₄	—	269	1	no	—
714	C₂²×C₄	—	269	1	no	—
715	C₂²×C₄	—	269	1	no	—
716	C₂²×C₄	—	269	1	no	—
717	C₂²×C₄	—	269	1	no	—
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	—	1076	2	no	—
732	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
733	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
734	C₄⋊C₄	—	269	1	no	—
735	C₄⋊C₄	—	269	1	no	—
736	C₄⋊C₄	—	269	1	no	—
737	C₄⋊C₄	—	269	1	no	—
738	C₄⋊C₄	—	269	1	no	—
739	C₄⋊C₄	—	269	1	no	—
740	C₄⋊C₄	—	269	1	no	—
741	C₄⋊C₄	—	269	1	no	—
742	C₄⋊C₄	—	269	1	no	—
743	C₄⋊C₄	—	269	1	no	—
744	C₄⋊C₄	—	269	1	no	—
745	C₄⋊C₄	—	269	1	no	—
746	C₄⋊C₄	—	269	1	no	—
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	C₂²×D₂₆₉	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
782	C₂²⋊C₄	—	269	1	no	—
783	C₂²⋊C₄	—	269	1	no	—
784	C₂²⋊C₄	—	269	1	no	—
785	C₂²⋊C₄	—	269	1	no	—
786	C₂²⋊C₄	—	269	1	no	—
787	C₂²⋊C₄	—	269	1	no	—
788	C₂²⋊C₄	—	269	1	no	—
789	C₂²⋊C₄	—	269	1	no	—
790	C₂²⋊C₄	—	269	1	no	—
791	C₂²⋊C₄	—	269	1	no	—
792	C₂²⋊C₄	—	269	1	no	—
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	C₂²×D₂₆₉	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
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	C₄²	—	269	1	no	—
827	C₄²	—	269	1	no	—
828	C₄²	—	269	1	no	—
829	C₄²	—	269	1	no	—
830	C₄²	—	269	1	no	—
831	C₄²	—	269	1	no	—
832	C₄²	—	269	1	no	—
833	C₄²	—	269	1	no	—
834	C₄²	—	269	1	no	—
835	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
836	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
837	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
838	C₂³	—	269	1	no	—
839	C₂³	—	269	1	no	—
840	C₂³	—	269	1	no	—
841	C₂³	—	269	1	no	—
842	C₂³	—	269	1	no	—
843	C₂³	—	538	2	no	—
844	C₂³	—	1076	1	no	—
845	C₂³	—	1076	1	no	—
846	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
847	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
848	Q₈	—	4	1	no	—
849	Q₈	—	4	1	no	—
850	Q₈	—	4	1	no	—
851	Q₈	—	538	2	no	—
852	Q₈	—	538	2	no	—
853	Q₈	—	538	2	no	—
854	Q₈	—	1076	1	no	—
855	Q₈	—	1076	1	no	—
856	Q₈	—	1076	1	no	—
857	Q₈	—	1076	1	no	—
858	D₄	—	4	1	no	—
859	D₄	—	538	2	no	—
860	D₄	—	538	2	no	—
861	D₄	—	538	2	no	—
862	D₄	—	538	2	no	—
863	D₄	—	538	2	no	—
864	D₄	—	1076	1	no	—
865	D₄	—	1076	1	no	—
866	D₄	—	1076	1	no	—
867	D₄	—	1076	1	no	—
868	D₄	—	1076	1	no	—
869	D₄	—	1076	1	no	—
870	D₄	—	1076	1	no	—
871	D₄	—	1076	1	no	—
872	D₄	—	1076	1	no	—
873	D₄	—	1076	1	no	—
874	D₄	—	1076	1	no	—
875	D₄	—	1076	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	269	1	no	—
879	C₂×C₄	—	269	1	no	—
880	C₂×C₄	—	269	1	no	—
881	C₂×C₄	—	269	1	no	—
882	C₂×C₄	—	269	1	no	—
883	C₂×C₄	—	269	1	no	—
884	C₂×C₄	—	269	1	no	—
885	C₂×C₄	—	269	1	no	—
886	C₂×C₄	—	269	1	no	—
887	C₂×C₄	—	269	1	no	—
888	C₂×C₄	—	269	1	no	—
889	C₂×C₄	—	538	2	no	—
890	C₂×C₄	—	538	2	no	—
891	C₂×C₄	—	538	2	no	—
892	C₂×C₄	—	538	2	no	—
893	C₂×C₄	—	538	2	no	—
894	C₂×C₄	—	1076	1	no	—
895	C₂×C₄	—	1076	1	no	—
896	C₂×C₄	—	1076	1	no	—
897	C₂×C₄	—	1076	1	no	—
898	C₂×C₄	—	1076	1	no	—
899	C₂×C₄	—	1076	1	no	—
900	C₂×C₄	—	1076	1	no	—
901	C₂×C₄	—	1076	1	no	—
902	C₂×C₄	—	1076	1	no	—
903	C₂×C₄	—	1076	1	no	—
904	C₂×C₄	—	1076	1	no	—
905	C₂×C₄	—	1076	1	no	—
906	C₂×C₄	—	1076	1	no	—
907	C₂×C₄	—	1076	1	no	—
908	C₂×C₄	—	1076	1	no	—
909	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
910	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	269	2	no	—
929	C₂²	—	538	1	no	—
930	C₂²	—	538	1	no	—
931	C₂²	—	538	1	no	—
932	C₂²	—	538	1	no	—
933	C₂²	—	538	1	no	—
934	C₂²	—	538	1	no	—
935	C₂²	—	538	1	no	—
936	C₂²	—	538	1	no	—
937	C₂²	—	538	1	no	—
938	C₂²	—	538	1	no	—
939	C₂²	—	538	1	no	—
940	C₂²	—	538	1	no	—
941	C₂²	—	538	1	no	—
942	C₂²	—	538	1	no	—
943	C₂²	—	1076	4	no	—
944	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	269	2	no	—
959	C₄	—	538	1	no	—
960	C₄	—	538	1	no	—
961	C₄	—	538	1	no	—
962	C₄	—	538	1	no	—
963	C₄	—	538	1	no	—
964	C₄	—	538	1	no	—
965	C₄	—	538	1	no	—
966	C₄	—	538	1	no	—
967	C₄	—	538	1	no	—
968	C₄	—	538	1	no	—
969	C₂	—	4	1	no	—
970	C₂	—	4	1	no	—
971	C₂	—	538	2	no	—
972	C₂	—	1076	1	no	—
973	C₂	—	1076	1	no	—
974	C₂	—	1076	1	no	—
975	C₂	—	1076	1	no	—
976	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
977	C₂	2₋¹⁺⁴×D₂₆₉	1	1	yes	characteristic
978	C₂	#31771442	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#563×C₂₆₉	C₂
hypercenter	#563	D₂₆₉
hypocenter	C₂₆₉	#3541
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #31771356	C₂	semidirect
2. #31771352	C₂	semidirect
3. #31771351	C₂	semidirect
4. #31771322	C₂	semidirect
5. #31771316	C₂	semidirect
6. #31771311	C₂	semidirect
7. #31771309	C₂	semidirect
8. #31771308	C₂	semidirect
9. #31771306	C₂	semidirect
10. #31771306	C₂	semidirect
11. #31771291	C₂	semidirect
12. #31771270	C₂	semidirect
13. #31771265	C₂	semidirect
14. #31771263	C₂	semidirect
15. #31771253	C₂	semidirect
16. #31771229	C₂	semidirect
17. #31771221	C₂	semidirect
18. #31771221	C₂	semidirect
19. #31771214	C₂	semidirect
20. #31771204	C₂	semidirect
21. #31771203	C₂	semidirect
22. #31771194	C₂	semidirect
23. #31771194	C₂	semidirect
24. #31771191	C₂	semidirect
25. #31771189	C₂	semidirect
26. #31771185	C₂	semidirect
27. #31771180	C₂	semidirect
28. #31771118	C₂	semidirect
29. #31771113	C₂	semidirect
30. C₂²⋊Q₈×D₂₆₉	C₂	semidirect
31. #563×C₂₆₉	C₂	semidirect
33. C₂×#16864402	C₂²	semidirect
36. C₂×Q₈×D₂₆₉	C₂²	semidirect
38. #22575452	C₂²	semidirect
39. #22575452	C₂²	semidirect
40. #22575452	C₂²	semidirect
41. #22575451	C₂²	semidirect
45. #22575448	C₂²	semidirect
46. #22575448	C₂²	semidirect
47. #22575448	C₂²	semidirect
48. #22575448	C₂²	semidirect
52. #22575444	C₂²	semidirect
53. #22575444	C₂²	semidirect
54. #22575444	C₂²	semidirect
55. #22575443	C₂²	semidirect
56. #22575443	C₂²	semidirect
57. #22575443	C₂²	semidirect
58. #22575443	C₂²	semidirect
60. #22575442	C₂²	semidirect
67. #22575439	C₂²	semidirect
68. #22575439	C₂²	semidirect
74. #22575438	C₂²	semidirect
75. #22575438	C₂²	semidirect
76. #22575438	C₂²	semidirect
77. #22575438	C₂²	semidirect
79. #22575437	C₂²	semidirect
80. #22575437	C₂²	semidirect
87. #22575433	C₂²	semidirect
88. #22575433	C₂²	semidirect
96. #22575431	C₂²	semidirect
97. #22575431	C₂²	semidirect
98. #22575431	C₂²	semidirect
99. #22575431	C₂²	semidirect
100. #22575431	C₂²	semidirect
101. #22575431	C₂²	semidirect
104. #22575430	C₂²	semidirect
105. #22575430	C₂²	semidirect
109. #22575429	C₂²	semidirect
110. #22575429	C₂²	semidirect
111. #22575429	C₂²	semidirect
117. #22575428	C₂²	semidirect
127. #22575426	C₂²	semidirect
128. #22575426	C₂²	semidirect
135. C₄×Dic₅₃₈	C₂²	semidirect
136. C₄×Dic₅₃₈	C₂²	semidirect
137. C₄×Dic₅₃₈	C₂²	semidirect
138. #22575418	C₂²	semidirect
139. #22575418	C₂²	semidirect
143. C₄×D₁₀₇₆	C₂²	semidirect
157. #22575413	C₂²	semidirect
158. #22575413	C₂²	semidirect
160. #22575411	C₂²	semidirect
161. #22575410	C₂²	semidirect
162. #22575410	C₂²	semidirect
164. C₂×#16864381	C₂²	semidirect
168. C₄⋊C₄×D₂₆₉	C₂²	semidirect
169. C₄⋊C₄×D₂₆₉	C₂²	semidirect
172. C₄⋊Q₈×C₂₆₉	C₂²	semidirect
173. C₄⋊Q₈×C₂₆₉	C₂²	semidirect
176. #126×C₂₆₉	C₂²	semidirect
177. #126×C₂₆₉	C₂²	semidirect
178. #125×C₂₆₉	C₂²	semidirect
179. #125×C₂₆₉	C₂²	semidirect
185. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
186. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
489. C₂₆₉	#3541	semidirect
492. #563	D₂₆₉	semidirect
532. C₄⋊Q₈	C₂×D₂₆₉	semidirect
533. C₄⋊Q₈	C₂×D₂₆₉	semidirect
546. #126	C₂×D₂₆₉	semidirect
547. #126	C₂×D₂₆₉	semidirect
555. #125	C₂×D₂₆₉	semidirect
556. #125	C₂×D₂₆₉	semidirect
615. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
616. C₂²⋊Q₈	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
#31771352	2
#31771351	2
#31771322	2
#31771316	2
#31771311	2
#31771309	2
#31771308	2
#31771306	2
#31771291	2
#31771270	2
#31771265	2
#31771263	2
#31771253	2
#31771229	2
#31771221	2
#31771214	2
#31771204	2
#31771203	2
#31771194	2
#31771191	2
#31771189	2
#31771185	2
#31771180	2
#31771118	2
#31771113	2
C₂²⋊Q₈×D₂₆₉	2
#563×C₂₆₉	2
#3541	269