Subgroups — #46825578

Order 34432.

958 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771358	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771357	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771356	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771348	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771326	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771325	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771324	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771322	C₂	1	1	yes	maximal, characteristic, complemented
9	#31771322	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771322	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771286	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771285	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771284	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771281	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771281	C₂	1	1	yes	maximal, characteristic, complemented
16	#31771278	C₂	1	1	yes	maximal, characteristic, complemented
17	#31771224	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771223	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771222	C₂	1	1	yes	maximal, characteristic, complemented
20	#31771222	C₂	1	1	yes	maximal, characteristic, complemented
21	#31771220	C₂	1	1	yes	maximal, characteristic, complemented
22	#31771219	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	#31771190	C₂	1	1	yes	maximal, characteristic, complemented
26	#31771187	C₂	1	1	yes	maximal, characteristic, complemented
27	#31771187	C₂	1	1	yes	maximal, characteristic, complemented
28	#31771136	C₂	1	1	yes	maximal, characteristic, complemented
29	#31771135	C₂	1	1	yes	maximal, characteristic, complemented
30	#31771132	C₂	1	1	yes	maximal, characteristic, complemented
31	#538×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
32	#22575453	C₂²	1	1	yes	characteristic, complemented
33	#22575452	C₂²	1	1	yes	characteristic, complemented
34	#22575452	C₂²	1	1	yes	characteristic, complemented
35	#22575452	C₂²	1	1	yes	characteristic, complemented
36	#22575452	C₂²	1	1	yes	characteristic, complemented
37	#22575451	C₂²	1	1	yes	characteristic, complemented
38	#22575448	C₂²	1	1	yes	characteristic, complemented
39	#22575448	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	#22575448	C₂²	1	1	yes	characteristic, complemented
44	#22575448	C₂²	1	1	yes	characteristic, complemented
45	#22575447	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	#22575446	C₂²	1	1	yes	characteristic, complemented
53	#22575446	C₂²	1	1	yes	characteristic, complemented
54	#22575446	C₂²	1	1	yes	characteristic, complemented
55	#22575446	C₂²	1	1	yes	characteristic, complemented
56	#22575446	C₂²	1	1	yes	characteristic, complemented
57	#22575446	C₂²	1	1	yes	characteristic, complemented
58	#22575446	C₂²	1	1	yes	characteristic, complemented
59	#22575446	C₂²	1	1	yes	characteristic, complemented
60	#22575446	C₂²	1	1	yes	characteristic, complemented
61	#22575446	C₂²	1	1	yes	characteristic, complemented
62	#22575444	C₂²	1	1	yes	characteristic, complemented
63	#22575443	C₂²	1	1	yes	characteristic, complemented
64	#22575443	C₂²	1	1	yes	characteristic, complemented
65	#22575440	C₂²	1	1	yes	characteristic
66	#22575440	C₂²	1	1	yes	characteristic
67	#22575440	C₂²	1	1	yes	characteristic
68	#22575440	C₂²	1	1	yes	characteristic
69	#22575440	C₂²	1	1	yes	characteristic, complemented
70	#22575440	C₂²	1	1	yes	characteristic, complemented
71	#22575440	C₂²	1	1	yes	characteristic, complemented
72	#22575439	C₂²	1	1	yes	characteristic
73	#22575439	C₂²	1	1	yes	characteristic
74	#22575439	C₂²	1	1	yes	characteristic
75	#22575439	C₂²	1	1	yes	characteristic
76	#22575439	C₂²	1	1	yes	characteristic
77	#22575439	C₂²	1	1	yes	characteristic
78	#22575439	C₂²	1	1	yes	characteristic
79	#22575439	C₂²	1	1	yes	characteristic
80	#22575439	C₂²	1	1	yes	characteristic
81	#22575439	C₂²	1	1	yes	characteristic
82	#22575439	C₂²	1	1	yes	characteristic, complemented
83	#22575439	C₂²	1	1	yes	characteristic, complemented
84	#22575437	C₂²	1	1	yes	characteristic
85	#22575437	C₂²	1	1	yes	characteristic
86	#22575437	C₂²	1	1	yes	characteristic, complemented
87	#22575436	C₂²	1	1	yes	characteristic
88	#22575436	C₂²	1	1	yes	characteristic
89	#22575436	C₂²	1	1	yes	characteristic, complemented
90	#22575435	C₂²	1	1	yes	characteristic
91	#22575435	C₂²	1	1	yes	characteristic
92	#22575435	C₂²	1	1	yes	characteristic
93	#22575435	C₂²	1	1	yes	characteristic
94	#22575434	C₂²	1	1	yes	characteristic
95	#22575434	C₂²	1	1	yes	characteristic
96	#22575434	C₂²	1	1	yes	characteristic
97	#22575434	C₂²	1	1	yes	characteristic, complemented
98	#22575434	C₂²	1	1	yes	characteristic, complemented
99	#22575434	C₂²	1	1	yes	characteristic, complemented
100	#22575433	C₂²	1	1	yes	characteristic, complemented
101	#22575432	C₂²	1	1	yes	characteristic, complemented
102	#22575432	C₂²	1	1	yes	characteristic, complemented
103	#22575432	C₂²	1	1	yes	characteristic, complemented
104	#22575432	C₂²	1	1	yes	characteristic, complemented
105	#22575432	C₂²	1	1	yes	characteristic, complemented
106	#22575431	C₂²	1	1	yes	characteristic, complemented
107	#22575431	C₂²	1	1	yes	characteristic, complemented
108	#22575431	C₂²	1	1	yes	characteristic, complemented
109	#22575430	C₂²	1	1	yes	characteristic, complemented
110	#22575430	C₂²	1	1	yes	characteristic, complemented
111	#22575430	C₂²	1	1	yes	characteristic, complemented
112	#22575430	C₂²	1	1	yes	characteristic, complemented
113	#22575430	C₂²	1	1	yes	characteristic, complemented
114	#22575430	C₂²	1	1	yes	characteristic, complemented
115	#22575430	C₂²	1	1	yes	characteristic, complemented
116	#22575430	C₂²	1	1	yes	characteristic, complemented
117	#22575430	C₂²	1	1	yes	characteristic, complemented
118	#22575429	C₂²	1	1	yes	characteristic, complemented
119	#22575429	C₂²	1	1	yes	characteristic, complemented
120	#22575425	C₂²	1	1	yes	characteristic
121	#22575425	C₂²	1	1	yes	characteristic
122	#22575425	C₂²	1	1	yes	characteristic
123	#22575425	C₂²	1	1	yes	characteristic
124	#22575424	C₂²	1	1	yes	characteristic
125	#22575424	C₂²	1	1	yes	characteristic
126	#22575422	C₂²	1	1	yes	characteristic
127	#22575422	C₂²	1	1	yes	characteristic
128	#22575421	C₂²	1	1	yes	characteristic
129	#22575421	C₂²	1	1	yes	characteristic
130	#22575421	C₂²	1	1	yes	characteristic
131	#22575421	C₂²	1	1	yes	characteristic, complemented
132	Q₈×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
133	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
134	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
135	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
136	#22575418	C₂²	1	1	yes	characteristic, complemented
137	#22575418	C₂²	1	1	yes	characteristic, complemented
138	#22575418	C₂²	1	1	yes	characteristic, complemented
139	#22575418	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
143	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
144	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
145	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
146	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
147	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
148	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
149	#22575413	C₂²	1	1	yes	characteristic
150	#22575413	C₂²	1	1	yes	characteristic
151	#22575413	C₂²	1	1	yes	characteristic
152	#22575413	C₂²	1	1	yes	characteristic
153	#22575413	C₂²	1	1	yes	characteristic, complemented
154	#22575412	C₂²	1	1	yes	characteristic, complemented
155	#22575412	C₂²	1	1	yes	characteristic, complemented
156	#22575412	C₂²	1	1	yes	characteristic, complemented
157	#22575411	C₂²	1	1	yes	characteristic, complemented
158	#22575410	C₂²	1	1	yes	characteristic, complemented
159	#22575410	C₂²	1	1	yes	characteristic, complemented
160	#22575410	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	#22575409	C₂²	1	1	yes	characteristic, complemented
165	#22575409	C₂²	1	1	yes	characteristic, complemented
166	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
167	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
168	C₂×#16864379	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
171	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
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
175	#124×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
176	#123×C₂₆₉	C₂²	1	1	yes	characteristic
177	#123×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
179	#121×C₂₆₉	C₂²	1	1	yes	characteristic
180	#121×C₂₆₉	C₂²	1	1	yes	characteristic
181	#121×C₂₆₉	C₂²	1	1	yes	characteristic
182	#120×C₂₆₉	C₂²	1	1	yes	characteristic
183	#120×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
185	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
188	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
189	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
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×Dic₅₃₈	C₂³	1	1	yes	characteristic
195	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
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	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
205	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
206	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
207	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
208	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
209	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
210	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
227	#16864381	C₂³	1	1	yes	characteristic
228	#16864381	C₂³	1	1	yes	characteristic
229	#16864381	C₂³	1	1	yes	characteristic
230	#16864381	C₂³	1	1	yes	characteristic
231	#16864381	C₂³	1	1	yes	characteristic
232	#16864381	C₂³	1	1	yes	characteristic
233	#16864381	C₂³	1	1	yes	characteristic
234	#16864381	C₂³	1	1	yes	characteristic
235	#16864381	C₂³	1	1	yes	characteristic
236	#16864381	C₂³	1	1	yes	characteristic
237	#16864381	C₂³	1	1	yes	characteristic
238	#16864381	C₂³	1	1	yes	characteristic
239	#16864381	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	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
252	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
253	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
254	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
255	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
256	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
257	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₂₆₉	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	#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	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
292	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
293	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
294	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
295	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
296	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
297	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
298	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
299	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
300	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
301	C₄×Dic₂₆₉	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	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
308	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
309	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
310	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
311	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
312	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
313	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
314	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
316	C₂²×C₄×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	C₂²×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	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	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
333	C₂²⋊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	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
341	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
342	C₂²×D₂₆₉	—	4	1	no	—
343	C₂²×D₂₆₉	—	4	1	no	—
344	C₂²×D₂₆₉	—	4	1	no	—
345	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
346	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
347	Dic₅₃₈	—	4	1	no	—
348	Dic₅₃₈	—	4	1	no	—
349	Dic₅₃₈	—	4	1	no	—
350	Dic₅₃₈	—	4	1	no	—
351	Dic₅₃₈	—	4	1	no	—
352	Dic₅₃₈	—	4	1	no	—
353	Dic₅₃₈	—	4	1	no	—
354	Dic₅₃₈	—	4	1	no	—
355	C₂²⋊D₂₆₉	—	4	1	no	—
356	C₂²⋊D₂₆₉	—	4	1	no	—
357	C₂²⋊D₂₆₉	—	4	1	no	—
358	C₂²⋊D₂₆₉	—	4	1	no	—
359	C₂²⋊D₂₆₉	—	4	1	no	—
360	C₂²⋊D₂₆₉	—	4	1	no	—
361	C₂²⋊D₂₆₉	—	4	1	no	—
362	C₂²⋊D₂₆₉	—	4	1	no	—
363	C₂×Dic₂₆₉	—	4	1	no	—
364	C₂×Dic₂₆₉	—	4	1	no	—
365	C₂×Dic₂₆₉	—	4	1	no	—
366	C₂×Dic₂₆₉	—	4	1	no	—
367	C₂×Dic₂₆₉	—	4	1	no	—
368	C₂×Dic₂₆₉	—	4	1	no	—
369	C₂×Dic₂₆₉	—	4	1	no	—
370	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
371	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
372	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
373	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
374	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
376	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
384	C₄×D₂₆₉	—	4	1	no	—
385	C₄×D₂₆₉	—	4	1	no	—
386	C₄×D₂₆₉	—	4	1	no	—
387	C₄×D₂₆₉	—	4	1	no	—
388	C₂³×C₂₆₉	—	4	1	no	—
389	C₂³×C₂₆₉	—	4	1	no	—
390	C₂³×C₂₆₉	—	4	1	no	—
391	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
392	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
393	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
394	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
395	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
396	Q₈×C₂₆₉	—	4	1	no	—
397	D₄×C₂₆₉	—	4	1	no	—
398	D₄×C₂₆₉	—	4	1	no	—
399	D₄×C₂₆₉	—	4	1	no	—
400	D₄×C₂₆₉	—	4	1	no	—
401	D₄×C₂₆₉	—	4	1	no	—
402	D₄×C₂₆₉	—	4	1	no	—
403	D₄×C₂₆₉	—	4	1	no	—
404	C₂×C₄×C₂₆₉	—	4	1	no	—
405	C₂×C₄×C₂₆₉	—	4	1	no	—
406	C₂×C₄×C₂₆₉	—	4	1	no	—
407	C₂×C₄×C₂₆₉	—	4	1	no	—
408	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
418	C₂²×C₂₆₉	—	2	1	no	—
419	C₂²×C₂₆₉	—	2	1	no	—
420	C₂²×C₂₆₉	—	2	1	no	—
421	C₂²×C₂₆₉	—	2	1	no	—
422	C₂²×C₂₆₉	—	2	1	no	—
423	C₂²×C₂₆₉	—	2	1	no	—
424	C₂²×C₂₆₉	—	2	1	no	—
425	C₂²×C₂₆₉	—	2	1	no	—
426	C₂²×C₂₆₉	—	2	1	no	—
427	C₂²×C₂₆₉	—	2	1	no	—
428	C₂²×C₂₆₉	—	2	1	no	—
429	C₂²×C₂₆₉	—	2	1	no	—
430	C₂²×C₂₆₉	—	2	1	no	—
431	C₂²×C₂₆₉	—	2	1	no	—
432	C₂²×C₂₆₉	—	2	1	no	—
433	C₂²×C₂₆₉	—	8	2	no	—
434	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
435	C₂×D₂₆₉	—	2	1	no	—
436	C₂×D₂₆₉	—	2	1	no	—
437	C₂×D₂₆₉	—	2	1	no	—
438	C₂×D₂₆₉	—	2	1	no	—
439	C₂×D₂₆₉	—	2	1	no	—
440	C₂×D₂₆₉	—	2	1	no	—
441	C₂×D₂₆₉	—	8	2	no	—
442	C₄×C₂₆₉	—	2	1	no	—
443	C₄×C₂₆₉	—	2	1	no	—
444	C₄×C₂₆₉	—	2	1	no	—
445	C₄×C₂₆₉	—	2	1	no	—
446	C₄×C₂₆₉	—	2	1	no	—
447	C₄×C₂₆₉	—	2	1	no	—
448	C₄×C₂₆₉	—	2	1	no	—
449	C₄×C₂₆₉	—	2	1	no	—
450	C₄×C₂₆₉	—	2	1	no	—
451	C₄×C₂₆₉	—	2	1	no	—
452	Dic₂₆₉	—	2	1	no	—
453	Dic₂₆₉	—	2	1	no	—
454	Dic₂₆₉	—	2	1	no	—
455	Dic₂₆₉	—	2	1	no	—
456	Dic₂₆₉	—	2	1	no	—
457	Dic₂₆₉	—	2	1	no	—
458	Dic₂₆₉	—	2	1	no	—
459	Dic₂₆₉	—	2	1	no	—
460	Dic₂₆₉	—	2	1	no	—
461	Dic₂₆₉	—	2	1	no	—
462	Dic₂₆₉	—	2	1	no	—
463	Dic₂₆₉	—	2	1	no	—
464	Dic₂₆₉	—	2	1	no	—
465	Dic₂₆₉	—	2	1	no	—
466	C₂×C₂₆₉	—	4	1	no	—
467	C₂×C₂₆₉	—	4	1	no	—
468	C₂×C₂₆₉	—	4	1	no	—
469	C₂×C₂₆₉	—	4	1	no	—
470	C₂×C₂₆₉	—	4	1	no	—
471	C₂×C₂₆₉	#585	1	1	yes	characteristic
472	C₂×C₂₆₉	#585	1	1	yes	characteristic
473	C₂×C₂₆₉	#585	1	1	yes	characteristic
474	D₂₆₉	—	4	1	no	—
475	D₂₆₉	—	4	1	no	—
476	C₂₆₉	#3568	1	1	yes	characteristic, complemented, Sylow
477	#3568	—	269	1	no	maximal, Sylow
478	#563	—	269	1	no	—
479	#563	—	269	1	no	—
480	#563	—	269	1	no	—
481	H(3,𝔽₄)	—	269	1	no	—
482	#556	—	269	1	no	—
483	#556	—	269	1	no	—
484	#556	—	269	1	no	—
485	#556	—	269	1	no	—
486	#556	—	269	1	no	—
487	#556	—	269	1	no	—
488	#551	—	269	1	no	—
489	#551	—	269	1	no	—
490	#551	—	269	1	no	—
491	#551	—	269	1	no	—
492	#551	—	269	1	no	—
493	#551	—	269	1	no	—
494	#542	—	269	1	no	—
495	#542	—	269	1	no	—
496	#542	—	269	1	no	—
497	#542	—	269	1	no	—
498	#542	—	269	1	no	—
499	#542	—	269	1	no	—
500	#538	—	269	1	no	—
501	#538	—	269	1	no	—
502	#538	—	269	1	no	—
503	#538	—	269	1	no	—
504	#538	—	269	1	no	—
505	#538	D₂₆₉	1	1	yes	characteristic, complemented
506	#529	—	269	1	no	—
507	#529	—	269	1	no	—
508	#529	—	269	1	no	—
509	C₄⋊Q₈	—	269	1	no	—
510	C₄⋊Q₈	—	269	1	no	—
511	C₄⋊Q₈	—	269	1	no	—
512	C₄⋊Q₈	—	269	1	no	—
513	C₄⋊Q₈	—	269	1	no	—
514	C₄⋊Q₈	—	269	1	no	—
515	#126	—	269	1	no	—
516	#126	—	269	1	no	—
517	#126	—	269	1	no	—
518	#126	—	269	1	no	—
519	#126	—	269	1	no	—
520	#126	—	269	1	no	—
521	#126	—	269	1	no	—
522	#126	—	269	1	no	—
523	#126	—	269	1	no	—
524	#126	—	269	1	no	—
525	#126	—	269	1	no	—
526	#126	—	269	1	no	—
527	#126	—	269	1	no	—
528	#126	—	269	1	no	—
529	#126	—	269	1	no	—
530	#126	—	269	1	no	—
531	#126	—	269	1	no	—
532	#126	—	269	1	no	—
533	#126	—	269	1	no	—
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	C₂×D₂₆₉	1	1	yes	characteristic, complemented
540	#126	C₂×D₂₆₉	1	1	yes	characteristic, complemented
541	#125	—	269	1	no	—
542	#125	—	269	1	no	—
543	#125	—	269	1	no	—
544	#124	—	269	1	no	—
545	#124	—	269	1	no	—
546	#124	—	269	1	no	—
547	#124	—	269	1	no	—
548	#124	—	269	1	no	—
549	#124	—	269	1	no	—
550	#124	—	269	1	no	—
551	#124	—	269	1	no	—
552	#124	—	269	1	no	—
553	#124	—	269	1	no	—
554	#124	—	269	1	no	—
555	#124	—	269	1	no	—
556	#124	—	269	1	no	—
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	C₂×D₂₆₉	1	1	yes	characteristic
564	#124	C₂×D₂₆₉	1	1	yes	characteristic, complemented
565	#123	—	269	1	no	—
566	#123	—	269	1	no	—
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	C₂×D₂₆₉	1	1	yes	characteristic
582	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
583	C₂²⋊Q₈	—	269	1	no	—
584	C₂²⋊Q₈	—	269	1	no	—
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	C₂×D₂₆₉	1	1	yes	characteristic, complemented
604	#121	—	269	1	no	—
605	#121	—	269	1	no	—
606	#121	—	269	1	no	—
607	#121	—	269	1	no	—
608	#121	—	269	1	no	—
609	#121	—	269	1	no	—
610	#121	C₂×D₂₆₉	1	1	yes	characteristic
611	#121	C₂×D₂₆₉	1	1	yes	characteristic
612	#121	C₂×D₂₆₉	1	1	yes	characteristic
613	#120	—	269	1	no	—
614	#120	—	269	1	no	—
615	#120	—	269	1	no	—
616	#120	—	269	1	no	—
617	#120	—	269	1	no	—
618	#120	—	269	1	no	—
619	#120	C₂×D₂₆₉	1	1	yes	characteristic
620	#120	C₂×D₂₆₉	1	1	yes	characteristic, complemented
621	C₄×Q₈	—	269	1	no	—
622	C₄×Q₈	—	269	1	no	—
623	C₄×Q₈	—	269	1	no	—
624	C₄×Q₈	—	269	1	no	—
625	C₄×Q₈	—	269	1	no	—
626	C₄×Q₈	—	269	1	no	—
627	C₄×Q₈	—	269	1	no	—
628	C₄×Q₈	—	269	1	no	—
629	C₄×Q₈	—	269	1	no	—
630	C₄×D₄	—	269	1	no	—
631	C₄×D₄	—	269	1	no	—
632	C₄×D₄	—	269	1	no	—
633	C₄×D₄	—	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	C₂×D₂₆₉	1	1	yes	characteristic
644	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
645	#117	—	269	1	no	—
646	#117	—	269	1	no	—
647	#117	—	269	1	no	—
648	#117	—	269	1	no	—
649	#117	—	269	1	no	—
650	#117	—	269	1	no	—
651	#117	—	269	1	no	—
652	#117	—	269	1	no	—
653	#117	—	269	1	no	—
654	#117	—	269	1	no	—
655	#117	—	269	1	no	—
656	#117	—	269	1	no	—
657	C₂×C₂²⋊C₄	—	269	1	no	—
658	C₂×C₂²⋊C₄	—	269	1	no	—
659	C₂×C₂²⋊C₄	—	269	1	no	—
660	C₂×C₂²⋊C₄	—	269	1	no	—
661	C₂×C₂²⋊C₄	—	269	1	no	—
662	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
663	C₂×C₄²	—	269	1	no	—
664	C₂⁴	—	269	1	no	—
665	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
666	C₂×Q₈	—	269	1	no	—
667	C₂×Q₈	—	269	1	no	—
668	C₂×Q₈	—	269	1	no	—
669	C₂×Q₈	—	269	1	no	—
670	C₂×Q₈	—	269	1	no	—
671	C₂×Q₈	—	269	1	no	—
672	C₂×Q₈	—	269	1	no	—
673	C₂×Q₈	—	269	1	no	—
674	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
675	C₂×D₄	—	269	1	no	—
676	C₂×D₄	—	269	1	no	—
677	C₂×D₄	—	269	1	no	—
678	C₂×D₄	—	269	1	no	—
679	C₂×D₄	—	269	1	no	—
680	C₂×D₄	—	269	1	no	—
681	C₂×D₄	—	269	1	no	—
682	C₂×D₄	—	269	1	no	—
683	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
684	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
685	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
686	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
687	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
688	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
689	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
690	C₂²×C₄	—	269	1	no	—
691	C₂²×C₄	—	269	1	no	—
692	C₂²×C₄	—	269	1	no	—
693	C₂²×C₄	—	269	1	no	—
694	C₂²×C₄	—	269	1	no	—
695	C₂²×C₄	—	269	1	no	—
696	C₂²×C₄	—	269	1	no	—
697	C₂²×C₄	—	269	1	no	—
698	C₂²×C₄	—	269	1	no	—
699	C₂²×C₄	—	269	1	no	—
700	C₂²×C₄	—	269	1	no	—
701	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
702	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
703	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
705	C₄⋊C₄	—	269	1	no	—
706	C₄⋊C₄	—	269	1	no	—
707	C₄⋊C₄	—	269	1	no	—
708	C₄⋊C₄	—	269	1	no	—
709	C₄⋊C₄	—	269	1	no	—
710	C₄⋊C₄	—	269	1	no	—
711	C₄⋊C₄	—	269	1	no	—
712	C₄⋊C₄	—	269	1	no	—
713	C₄⋊C₄	—	269	1	no	—
714	C₄⋊C₄	—	269	1	no	—
715	C₄⋊C₄	—	269	1	no	—
716	C₄⋊C₄	—	269	1	no	—
717	C₄⋊C₄	—	269	1	no	—
718	C₄⋊C₄	—	269	1	no	—
719	C₄⋊C₄	—	269	1	no	—
720	C₄⋊C₄	—	269	1	no	—
721	C₄⋊C₄	—	269	1	no	—
722	C₄⋊C₄	—	269	1	no	—
723	C₄⋊C₄	—	269	1	no	—
724	C₄⋊C₄	—	269	1	no	—
725	C₄⋊C₄	—	269	1	no	—
726	C₄⋊C₄	—	269	1	no	—
727	C₄⋊C₄	—	269	1	no	—
728	C₄⋊C₄	—	269	1	no	—
729	C₄⋊C₄	—	269	1	no	—
730	C₄⋊C₄	—	269	1	no	—
731	C₄⋊C₄	—	269	1	no	—
732	C₄⋊C₄	—	269	1	no	—
733	C₄⋊C₄	—	269	1	no	—
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	C₂²×D₂₆₉	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
746	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
747	C₂²⋊C₄	—	269	1	no	—
748	C₂²⋊C₄	—	269	1	no	—
749	C₂²⋊C₄	—	269	1	no	—
750	C₂²⋊C₄	—	269	1	no	—
751	C₂²⋊C₄	—	269	1	no	—
752	C₂²⋊C₄	—	269	1	no	—
753	C₂²⋊C₄	—	269	1	no	—
754	C₂²⋊C₄	—	269	1	no	—
755	C₂²⋊C₄	—	269	1	no	—
756	C₂²⋊C₄	—	269	1	no	—
757	C₂²⋊C₄	—	269	1	no	—
758	C₂²⋊C₄	—	269	1	no	—
759	C₂²⋊C₄	—	269	1	no	—
760	C₂²⋊C₄	—	269	1	no	—
761	C₂²⋊C₄	—	269	1	no	—
762	C₂²⋊C₄	—	269	1	no	—
763	C₂²⋊C₄	—	269	1	no	—
764	C₂²⋊C₄	—	269	1	no	—
765	C₂²⋊C₄	—	269	1	no	—
766	C₂²⋊C₄	—	269	1	no	—
767	C₂²⋊C₄	—	269	1	no	—
768	C₂²⋊C₄	—	269	1	no	—
769	C₂²⋊C₄	—	269	1	no	—
770	C₂²⋊C₄	—	269	1	no	—
771	C₂²⋊C₄	—	269	1	no	—
772	C₂²⋊C₄	—	269	1	no	—
773	C₂²⋊C₄	—	269	1	no	—
774	C₂²⋊C₄	—	269	1	no	—
775	C₂²⋊C₄	—	269	1	no	—
776	C₂²⋊C₄	—	269	1	no	—
777	C₂²⋊C₄	—	269	1	no	—
778	C₂²⋊C₄	—	269	1	no	—
779	C₂²⋊C₄	—	269	1	no	—
780	C₂²⋊C₄	—	269	1	no	—
781	C₂²⋊C₄	—	269	1	no	—
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	C₂²×D₂₆₉	1	1	yes	characteristic
788	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
789	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
790	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
791	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
792	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
801	C₄²	—	269	1	no	—
802	C₄²	—	269	1	no	—
803	C₄²	—	269	1	no	—
804	C₄²	—	269	1	no	—
805	C₄²	—	269	1	no	—
806	C₄²	—	269	1	no	—
807	C₄²	—	269	1	no	—
808	C₄²	—	269	1	no	—
809	C₄²	—	269	1	no	—
810	C₄²	—	269	1	no	—
811	C₄²	—	269	1	no	—
812	C₄²	—	269	1	no	—
813	C₄²	—	269	1	no	—
814	C₄²	—	269	1	no	—
815	C₄²	—	269	1	no	—
816	C₄²	—	269	1	no	—
817	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
818	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	4	1	no	—
822	C₂³	—	269	1	no	—
823	C₂³	—	269	1	no	—
824	C₂³	—	1076	1	no	—
825	C₂³	—	1076	1	no	—
826	C₂³	—	1076	1	no	—
827	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
828	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
829	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
830	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
831	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
832	Q₈	—	4	1	no	—
833	Q₈	—	1076	1	no	—
834	Q₈	—	1076	1	no	—
835	Q₈	—	1076	1	no	—
836	Q₈	—	1076	1	no	—
837	Q₈	—	1076	1	no	—
838	Q₈	—	1076	1	no	—
839	Q₈	—	1076	1	no	—
840	Q₈	—	1076	1	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	4	1	no	—
848	D₄	—	1076	1	no	—
849	D₄	—	1076	1	no	—
850	D₄	—	1076	1	no	—
851	D₄	—	1076	1	no	—
852	D₄	—	1076	1	no	—
853	D₄	—	1076	1	no	—
854	D₄	—	1076	1	no	—
855	D₄	—	1076	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	269	1	no	—
861	C₂×C₄	—	269	1	no	—
862	C₂×C₄	—	269	1	no	—
863	C₂×C₄	—	269	1	no	—
864	C₂×C₄	—	269	1	no	—
865	C₂×C₄	—	269	1	no	—
866	C₂×C₄	—	269	1	no	—
867	C₂×C₄	—	269	1	no	—
868	C₂×C₄	—	269	1	no	—
869	C₂×C₄	—	269	1	no	—
870	C₂×C₄	—	269	1	no	—
871	C₂×C₄	—	269	1	no	—
872	C₂×C₄	—	269	1	no	—
873	C₂×C₄	—	269	1	no	—
874	C₂×C₄	—	1076	1	no	—
875	C₂×C₄	—	1076	1	no	—
876	C₂×C₄	—	1076	1	no	—
877	C₂×C₄	—	1076	1	no	—
878	C₂×C₄	—	1076	1	no	—
879	C₂×C₄	—	1076	1	no	—
880	C₂×C₄	—	1076	1	no	—
881	C₂×C₄	—	1076	1	no	—
882	C₂×C₄	—	1076	1	no	—
883	C₂×C₄	—	1076	1	no	—
884	C₂×C₄	—	1076	1	no	—
885	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
894	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	8	2	no	—
911	C₂²	—	538	1	no	—
912	C₂²	—	538	1	no	—
913	C₂²	—	538	1	no	—
914	C₂²	—	538	1	no	—
915	C₂²	—	538	1	no	—
916	C₂²	—	538	1	no	—
917	C₂²	—	2152	2	no	—
918	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	538	1	no	—
930	C₄	—	538	1	no	—
931	C₄	—	538	1	no	—
932	C₄	—	538	1	no	—
933	C₄	—	538	1	no	—
934	C₄	—	538	1	no	—
935	C₄	—	538	1	no	—
936	C₄	—	538	1	no	—
937	C₄	—	538	1	no	—
938	C₄	—	538	1	no	—
939	C₄	—	538	1	no	—
940	C₄	—	538	1	no	—
941	C₄	—	538	1	no	—
942	C₄	—	538	1	no	—
943	C₂	—	4	1	no	—
944	C₂	—	4	1	no	—
945	C₂	—	4	1	no	—
946	C₂	—	4	1	no	—
947	C₂	—	4	1	no	—
948	C₂	—	1076	1	no	—
949	C₂	—	1076	1	no	—
950	C₂	#31771440	1	1	yes	characteristic
951	C₂	#31771440	1	1	yes	characteristic
952	C₂	#31771441	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#538×C₂₆₉	C₂
hypercenter	#538	D₂₆₉
hypocenter	C₂₆₉	#3568
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #31771358	C₂	semidirect
2. #31771357	C₂	semidirect
3. #31771356	C₂	semidirect
4. #31771348	C₂	semidirect
5. #31771326	C₂	semidirect
6. #31771325	C₂	semidirect
7. #31771324	C₂	semidirect
8. #31771322	C₂	semidirect
9. #31771322	C₂	semidirect
10. #31771322	C₂	semidirect
11. #31771286	C₂	semidirect
12. #31771285	C₂	semidirect
13. #31771284	C₂	semidirect
14. #31771281	C₂	semidirect
15. #31771281	C₂	semidirect
16. #31771278	C₂	semidirect
17. #31771224	C₂	semidirect
18. #31771223	C₂	semidirect
19. #31771222	C₂	semidirect
20. #31771222	C₂	semidirect
21. #31771220	C₂	semidirect
22. #31771219	C₂	semidirect
23. #31771192	C₂	semidirect
24. #31771190	C₂	semidirect
25. #31771190	C₂	semidirect
26. #31771187	C₂	semidirect
27. #31771187	C₂	semidirect
28. #31771136	C₂	semidirect
29. #31771135	C₂	semidirect
30. #31771132	C₂	semidirect
31. #538×C₂₆₉	C₂	semidirect
32. #22575453	C₂²	semidirect
33. #22575452	C₂²	semidirect
34. #22575452	C₂²	semidirect
35. #22575452	C₂²	semidirect
36. #22575452	C₂²	semidirect
37. #22575451	C₂²	semidirect
38. #22575448	C₂²	semidirect
39. #22575448	C₂²	semidirect
40. #22575448	C₂²	semidirect
41. #22575448	C₂²	semidirect
42. #22575448	C₂²	semidirect
43. #22575448	C₂²	semidirect
44. #22575448	C₂²	semidirect
45. #22575447	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. #22575446	C₂²	semidirect
53. #22575446	C₂²	semidirect
54. #22575446	C₂²	semidirect
55. #22575446	C₂²	semidirect
56. #22575446	C₂²	semidirect
57. #22575446	C₂²	semidirect
58. #22575446	C₂²	semidirect
59. #22575446	C₂²	semidirect
60. #22575446	C₂²	semidirect
61. #22575446	C₂²	semidirect
62. #22575444	C₂²	semidirect
63. #22575443	C₂²	semidirect
64. #22575443	C₂²	semidirect
69. #22575440	C₂²	semidirect
70. #22575440	C₂²	semidirect
71. #22575440	C₂²	semidirect
82. #22575439	C₂²	semidirect
83. #22575439	C₂²	semidirect
86. #22575437	C₂²	semidirect
89. #22575436	C₂²	semidirect
97. #22575434	C₂²	semidirect
98. #22575434	C₂²	semidirect
99. #22575434	C₂²	semidirect
100. #22575433	C₂²	semidirect
101. #22575432	C₂²	semidirect
102. #22575432	C₂²	semidirect
103. #22575432	C₂²	semidirect
104. #22575432	C₂²	semidirect
105. #22575432	C₂²	semidirect
106. #22575431	C₂²	semidirect
107. #22575431	C₂²	semidirect
108. #22575431	C₂²	semidirect
109. #22575430	C₂²	semidirect
110. #22575430	C₂²	semidirect
111. #22575430	C₂²	semidirect
112. #22575430	C₂²	semidirect
113. #22575430	C₂²	semidirect
114. #22575430	C₂²	semidirect
115. #22575430	C₂²	semidirect
116. #22575430	C₂²	semidirect
117. #22575430	C₂²	semidirect
118. #22575429	C₂²	semidirect
119. #22575429	C₂²	semidirect
131. #22575421	C₂²	semidirect
132. Q₈×Dic₂₆₉	C₂²	semidirect
133. C₄×Dic₅₃₈	C₂²	semidirect
134. C₄×Dic₅₃₈	C₂²	semidirect
135. C₄×Dic₅₃₈	C₂²	semidirect
136. #22575418	C₂²	semidirect
137. #22575418	C₂²	semidirect
138. #22575418	C₂²	semidirect
139. #22575418	C₂²	semidirect
140. #22575418	C₂²	semidirect
143. D₄×Dic₂₆₉	C₂²	semidirect
144. D₄×Dic₂₆₉	C₂²	semidirect
145. D₄×Dic₂₆₉	C₂²	semidirect
148. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
153. #22575413	C₂²	semidirect
154. #22575412	C₂²	semidirect
155. #22575412	C₂²	semidirect
156. #22575412	C₂²	semidirect
157. #22575411	C₂²	semidirect
158. #22575410	C₂²	semidirect
159. #22575410	C₂²	semidirect
160. #22575410	C₂²	semidirect
161. #22575409	C₂²	semidirect
162. #22575409	C₂²	semidirect
163. #22575409	C₂²	semidirect
164. #22575409	C₂²	semidirect
165. #22575409	C₂²	semidirect
166. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
167. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
168. C₂×#16864379	C₂²	semidirect
169. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
170. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
171. C₂×C₄×Dic₂₆₉	C₂²	semidirect
172. #126×C₂₆₉	C₂²	semidirect
173. #126×C₂₆₉	C₂²	semidirect
175. #124×C₂₆₉	C₂²	semidirect
177. #123×C₂₆₉	C₂²	semidirect
178. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
183. #120×C₂₆₉	C₂²	semidirect
185. C₄×D₄×C₂₆₉	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
476. C₂₆₉	#3568	semidirect
505. #538	D₂₆₉	semidirect
539. #126	C₂×D₂₆₉	semidirect
540. #126	C₂×D₂₆₉	semidirect
564. #124	C₂×D₂₆₉	semidirect
582. #123	C₂×D₂₆₉	semidirect
603. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
620. #120	C₂×D₂₆₉	semidirect
644. C₄×D₄	C₂×D₂₆₉	semidirect
662. 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
#31771358	2
#31771357	2
#31771356	2
#31771348	2
#31771326	2
#31771325	2
#31771324	2
#31771322	2
#31771286	2
#31771285	2
#31771284	2
#31771281	2
#31771278	2
#31771224	2
#31771223	2
#31771222	2
#31771220	2
#31771219	2
#31771192	2
#31771190	2
#31771187	2
#31771136	2
#31771135	2
#31771132	2
#538×C₂₆₉	2
#3568	269