Subgroups — #46824515

Order 34432.

1900 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771248	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771247	C₂	1	2	yes	maximal, complemented
5	#31771246	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771245	C₂	1	2	yes	maximal, complemented
7	#31771243	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×D₁₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×D₁₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771239	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771239	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771237	C₂	1	2	yes	maximal, complemented
14	#31771173	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771171	C₂	1	1	yes	maximal, characteristic, complemented
16	#31771166	C₂	1	2	yes	maximal, complemented
17	#31771163	C₂	1	2	yes	maximal, complemented
18	#31771118	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771114	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#22575423	C₂	1	2	yes	maximal, complemented
21	#120×D₂₆₉	C₂	1	2	yes	maximal, complemented
22	#31771077	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×D₂₆₉	C₂²	1	2	yes	complemented
25	#22575499	—	2	8	no	—
26	C₂×#16864403	C₂²	1	1	yes	characteristic, complemented
27	C₂×#16864403	C₂²	1	1	yes	characteristic, complemented
28	C₂×#16864402	C₂²	1	1	yes	characteristic, complemented
29	C₂×#16864402	C₂²	1	2	yes	complemented
30	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₁₀₇₆	C₂²	1	2	yes	complemented
32	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₁₀₇₆	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
36	C₂×D₄×D₂₆₉	—	2	8	no	—
37	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
39	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
41	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
45	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
46	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
47	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
48	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
49	#22575450	C₂²	1	1	yes	characteristic, complemented
50	#22575449	C₂²	1	1	yes	characteristic, complemented
51	#22575449	C₂²	1	2	yes	complemented
52	#22575442	C₂²	1	1	yes	characteristic, complemented
53	#22575439	C₂²	1	2	yes	complemented
54	#22575438	C₂²	1	2	yes	complemented
55	#22575438	C₂²	1	1	yes	characteristic, complemented
56	#22575438	C₂²	1	2	yes	complemented
57	#22575436	C₂²	1	2	yes	complemented
58	#22575435	C₂²	1	1	yes	characteristic, complemented
59	#22575435	C₂²	1	2	yes	complemented
60	#22575431	C₂²	1	1	yes	characteristic, complemented
61	#22575430	C₂²	1	1	yes	characteristic, complemented
62	#22575429	C₂²	1	1	yes	characteristic, complemented
63	#22575428	C₂²	1	1	yes	characteristic, complemented
64	#22575428	C₂²	1	2	yes	complemented
65	#22575428	C₂²	1	2	yes	complemented
66	#22575428	C₂²	1	1	yes	characteristic, complemented
67	#22575427	C₂²	1	1	yes	characteristic, complemented
68	#22575427	C₂²	1	2	yes	complemented
69	#22575427	C₂²	1	1	yes	characteristic, complemented
70	#22575426	C₂²	1	1	yes	characteristic, complemented
71	#22575426	C₂²	1	2	yes	complemented
72	#22575426	C₂²	1	2	yes	complemented
73	#22575426	C₂²	1	2	yes	complemented
74	#22575426	C₂²	1	2	yes	complemented
75	#22575425	C₂²	1	1	yes	characteristic, complemented
76	#22575425	C₂²	1	2	yes	complemented
77	#22575425	C₂²	1	2	yes	complemented
78	#22575424	C₂²	1	1	yes	characteristic, complemented
79	#22575423	C₂²	1	2	yes	complemented
80	#22575423	C₂²	1	1	yes	characteristic, complemented
81	#22575423	C₂²	1	2	yes	complemented
82	#22575423	C₂²	1	2	yes	complemented
83	#22575423	C₂²	1	2	yes	complemented
84	#22575423	C₂²	1	2	yes	complemented
85	#22575423	C₂²	1	2	yes	complemented
86	#22575423	C₂²	1	2	yes	complemented
87	#22575423	C₂²	1	2	yes	complemented
88	#22575423	C₂²	1	2	yes	complemented
89	#22575423	C₂²	1	2	yes	complemented
90	#22575423	C₂²	1	2	yes	complemented
91	#22575422	C₂²	1	2	yes	complemented
92	#22575421	C₂²	1	1	yes	characteristic, complemented
93	#22575421	C₂²	1	2	yes	complemented
94	#22575421	C₂²	1	2	yes	complemented
95	#22575421	C₂²	1	2	yes	complemented
96	#22575421	C₂²	1	2	yes	complemented
97	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
99	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
100	#22575415	C₂²	1	2	yes	complemented
101	#22575415	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
105	#22575413	C₂²	1	2	yes	complemented
106	#22575413	C₂²	1	2	yes	complemented
107	#22575411	C₂²	1	1	yes	characteristic, complemented
108	#22575410	C₂²	1	1	yes	characteristic, complemented
109	C₂×#16864379	C₂²	1	2	yes	complemented
110	C₂×#16864379	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
114	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
116	#124×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
117	#123×C₂₆₉	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₂₆₉	C₂²	1	2	yes	complemented
120	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
121	#120×C₂₆₉	C₂²	1	2	yes	complemented
122	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
125	C₂³×D₂₆₉	—	2	8	no	—
126	C₂³×D₂₆₉	—	4	4	no	—
127	C₂³×D₂₆₉	—	4	4	no	—
128	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
129	C₂³×D₂₆₉	C₂³	1	2	yes	—
130	C₂³×D₂₆₉	C₂³	1	2	yes	—
131	C₂³×D₂₆₉	C₂³	1	2	yes	—
132	C₂³×D₂₆₉	C₂³	1	2	yes	—
133	C₂³×D₂₆₉	C₂³	1	2	yes	—
134	C₂³×D₂₆₉	C₂³	1	2	yes	complemented
135	C₂³×D₂₆₉	C₂³	1	2	yes	complemented
136	#16864403	—	2	4	no	—
137	#16864403	—	2	4	no	—
138	#16864402	—	2	8	no	—
139	#16864402	—	2	4	no	—
140	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic, complemented
141	C₂×D₁₀₇₆	—	2	8	no	—
142	C₂×D₁₀₇₆	—	2	4	no	—
143	C₂×D₁₀₇₆	—	2	4	no	—
144	C₂×D₁₀₇₆	—	4	4	no	—
145	C₂×D₁₀₇₆	C₂³	1	2	yes	—
146	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
147	C₂×D₁₀₇₆	C₂³	1	2	yes	—
148	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
149	C₂×D₁₀₇₆	C₂³	1	2	yes	—
150	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
151	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
152	C₂×D₁₀₇₆	C₂³	1	2	yes	complemented
153	C₂×D₁₀₇₆	C₂³	1	2	yes	complemented
154	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic, complemented
155	C₂×D₁₀₇₆	C₂³	1	2	yes	complemented
156	C₂×D₁₀₇₆	C₂³	1	2	yes	complemented
157	C₂×D₁₀₇₆	C₂³	1	2	yes	complemented
158	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
159	C₂×C₂²⋊D₂₆₉	—	4	4	no	—
160	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	complemented
169	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic, complemented
170	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	complemented
171	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	complemented
172	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	complemented
173	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	complemented
174	D₄×D₂₆₉	—	2	8	no	—
175	D₄×D₂₆₉	—	2	8	no	—
176	D₄×D₂₆₉	—	2	4	no	—
177	D₄×D₂₆₉	—	2	8	no	—
178	D₄×D₂₆₉	—	2	8	no	—
179	D₄×D₂₆₉	—	2	4	no	—
180	D₄×D₂₆₉	—	2	4	no	—
181	D₄×D₂₆₉	—	2	4	no	—
182	D₄×D₂₆₉	—	4	4	no	—
183	D₄×D₂₆₉	—	4	4	no	—
184	D₄×D₂₆₉	D₄	1	8	yes	complemented
185	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
186	C₂²×Dic₂₆₉	C₂³	1	2	yes	complemented
187	C₂×C₄×D₂₆₉	—	2	4	no	—
188	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
189	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
190	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
191	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
192	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
193	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
194	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic, complemented
195	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
196	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
197	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic, complemented
198	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic, complemented
199	#16864381	C₂³	1	1	yes	characteristic, complemented
200	#16864381	C₂³	1	1	yes	characteristic, complemented
201	#16864381	C₂³	1	2	yes	complemented
202	#16864381	C₂³	1	1	yes	characteristic, complemented
203	#16864381	C₂³	1	1	yes	characteristic, complemented
204	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
205	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	complemented
206	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	complemented
207	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic, complemented
208	#16864379	C₂³	1	1	yes	characteristic
209	#16864379	C₂³	1	1	yes	characteristic
210	#16864379	C₂³	1	2	yes	—
211	#16864379	C₂³	1	2	yes	—
212	#16864379	C₂³	1	1	yes	characteristic
213	#16864379	C₂³	1	1	yes	characteristic
214	#16864379	C₂³	1	2	yes	complemented
215	#16864379	C₂³	1	2	yes	complemented
216	#16864379	C₂³	1	2	yes	complemented
217	#16864379	C₂³	1	2	yes	complemented
218	#16864379	C₂³	1	2	yes	complemented
219	#16864379	C₂³	1	2	yes	complemented
220	#16864379	C₂³	1	2	yes	complemented
221	#16864379	C₂³	1	1	yes	characteristic, complemented
222	#16864379	C₂³	1	2	yes	complemented
223	#16864379	C₂³	1	1	yes	characteristic, complemented
224	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic, complemented
225	C₄×Dic₂₆₉	C₂³	1	2	yes	complemented
226	C₂⁴×C₂₆₉	C₂³	1	2	yes	—
227	#41×C₂₆₉	—	2	4	no	—
228	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
229	C₂×D₄×C₂₆₉	—	2	4	no	—
230	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
231	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
232	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
233	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
234	C₂×D₄×C₂₆₉	C₂³	1	2	yes	complemented
235	C₂×D₄×C₂₆₉	C₂³	1	2	yes	complemented
236	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
237	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	complemented
238	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
239	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	complemented
240	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
241	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
242	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
243	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
244	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
245	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
246	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
247	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
248	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
249	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
250	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
251	C₂²×D₂₆₉	—	2	2	no	—
252	C₂²×D₂₆₉	—	2	2	no	—
253	C₂²×D₂₆₉	—	2	2	no	—
254	C₂²×D₂₆₉	—	2	4	no	—
255	C₂²×D₂₆₉	—	2	4	no	—
256	C₂²×D₂₆₉	—	2	4	no	—
257	C₂²×D₂₆₉	—	2	4	no	—
258	C₂²×D₂₆₉	—	2	4	no	—
259	C₂²×D₂₆₉	—	2	4	no	—
260	C₂²×D₂₆₉	—	2	4	no	—
261	C₂²×D₂₆₉	—	2	4	no	—
262	C₂²×D₂₆₉	—	2	4	no	—
263	C₂²×D₂₆₉	—	4	2	no	—
264	C₂²×D₂₆₉	—	4	2	no	—
265	C₂²×D₂₆₉	—	4	2	no	—
266	C₂²×D₂₆₉	—	4	2	no	—
267	C₂²×D₂₆₉	—	4	2	no	—
268	C₂²×D₂₆₉	—	4	2	no	—
269	C₂²×D₂₆₉	—	4	2	no	—
270	C₂²×D₂₆₉	—	4	2	no	—
271	C₂²×D₂₆₉	—	4	2	no	—
272	C₂²×D₂₆₉	—	4	2	no	—
273	C₂²×D₂₆₉	—	4	2	no	—
274	C₂²×D₂₆₉	—	4	32	no	—
275	C₂²×D₂₆₉	C₂×D₄	1	8	yes	complemented
276	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
277	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
278	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
279	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
280	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
281	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
282	Dic₅₃₈	—	2	2	no	—
283	D₁₀₇₆	—	2	4	no	—
284	D₁₀₇₆	—	2	4	no	—
285	D₁₀₇₆	—	2	4	no	—
286	D₁₀₇₆	—	2	2	no	—
287	D₁₀₇₆	—	2	4	no	—
288	D₁₀₇₆	—	2	4	no	—
289	D₁₀₇₆	—	2	2	no	—
290	D₁₀₇₆	—	2	2	no	—
291	D₁₀₇₆	—	2	2	no	—
292	D₁₀₇₆	—	4	2	no	—
293	D₁₀₇₆	—	4	2	no	—
294	D₁₀₇₆	—	4	2	no	—
295	D₁₀₇₆	C₂×D₄	1	4	yes	complemented
296	C₂²⋊D₂₆₉	—	2	4	no	—
297	C₂²⋊D₂₆₉	—	2	4	no	—
298	C₂²⋊D₂₆₉	—	2	4	no	—
299	C₂²⋊D₂₆₉	—	2	2	no	—
300	C₂²⋊D₂₆₉	—	2	4	no	—
301	C₂²⋊D₂₆₉	—	2	2	no	—
302	C₂²⋊D₂₆₉	—	2	2	no	—
303	C₂²⋊D₂₆₉	—	2	4	no	—
304	C₂²⋊D₂₆₉	—	2	2	no	—
305	C₂²⋊D₂₆₉	—	4	2	no	—
306	C₂²⋊D₂₆₉	—	4	2	no	—
307	C₂²⋊D₂₆₉	—	4	2	no	—
308	C₂²⋊D₂₆₉	—	4	2	no	—
309	C₂²⋊D₂₆₉	C₂×D₄	1	8	yes	complemented
310	C₂×Dic₂₆₉	—	2	2	no	—
311	C₂×Dic₂₆₉	—	4	2	no	—
312	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
313	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
314	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
315	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
316	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
317	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
318	C₄×D₂₆₉	—	2	2	no	—
319	C₄×D₂₆₉	—	2	4	no	—
320	C₄×D₂₆₉	—	2	2	no	—
321	C₄×D₂₆₉	—	2	2	no	—
322	C₄×D₂₆₉	—	2	2	no	—
323	C₄×D₂₆₉	—	2	4	no	—
324	C₄×D₂₆₉	—	4	2	no	—
325	C₄×D₂₆₉	—	4	2	no	—
326	C₄×D₂₆₉	C₂×D₄	1	4	yes	complemented
327	C₂³×C₂₆₉	—	2	4	no	—
328	C₂³×C₂₆₉	—	2	4	no	—
329	C₂³×C₂₆₉	—	4	2	no	—
330	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
331	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
332	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
333	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
334	Q₈×C₂₆₉	—	2	2	no	—
335	D₄×C₂₆₉	—	2	4	no	—
336	D₄×C₂₆₉	—	2	4	no	—
337	D₄×C₂₆₉	—	2	2	no	—
338	D₄×C₂₆₉	—	2	2	no	—
339	D₄×C₂₆₉	—	4	2	no	—
340	D₄×C₂₆₉	C₂×D₄	1	4	yes	complemented
341	C₂×C₄×C₂₆₉	—	2	4	no	—
342	C₂×C₄×C₂₆₉	—	2	2	no	—
343	C₂×C₄×C₂₆₉	—	2	2	no	—
344	C₂×C₄×C₂₆₉	—	4	2	no	—
345	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
346	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
347	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
348	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
349	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
350	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
351	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
352	C₂²×C₂₆₉	—	2	1	no	—
353	C₂²×C₂₆₉	—	2	2	no	—
354	C₂²×C₂₆₉	—	2	2	no	—
355	C₂²×C₂₆₉	—	2	1	no	—
356	C₂²×C₂₆₉	—	2	1	no	—
357	C₂²×C₂₆₉	—	2	2	no	—
358	C₂²×C₂₆₉	—	2	1	no	—
359	C₂²×C₂₆₉	—	2	1	no	—
360	C₂²×C₂₆₉	—	2	2	no	—
361	C₂²×C₂₆₉	—	2	2	no	—
362	C₂²×C₂₆₉	—	4	8	no	—
363	C₂²×C₂₆₉	C₂²×D₄	1	4	yes	—
364	C₂²×C₂₆₉	H(5,𝔽₂)	1	2	yes	complemented
365	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
366	C₂×D₂₆₉	—	2	8	no	—
367	C₂×D₂₆₉	—	2	1	no	—
368	C₂×D₂₆₉	—	2	2	no	—
369	C₂×D₂₆₉	—	2	2	no	—
370	C₂×D₂₆₉	—	2	1	no	—
371	C₂×D₂₆₉	—	2	1	no	—
372	C₂×D₂₆₉	—	2	1	no	—
373	C₂×D₂₆₉	—	2	1	no	—
374	C₂×D₂₆₉	—	2	2	no	—
375	C₂×D₂₆₉	—	2	2	no	—
376	C₂×D₂₆₉	—	2	1	no	—
377	C₂×D₂₆₉	—	2	2	no	—
378	C₂×D₂₆₉	—	2	2	no	—
379	C₂×D₂₆₉	—	2	2	no	—
380	C₂×D₂₆₉	—	2	1	no	—
381	C₂×D₂₆₉	—	2	2	no	—
382	C₂×D₂₆₉	—	4	8	no	—
383	C₂×D₂₆₉	—	4	8	no	—
384	C₂×D₂₆₉	—	4	8	no	—
385	C₂×D₂₆₉	—	4	8	no	—
386	C₂×D₂₆₉	—	4	8	no	—
387	C₂×D₂₆₉	—	8	4	no	—
388	C₂×D₂₆₉	—	8	4	no	—
389	C₂×D₂₆₉	C₂²×D₄	1	2	yes	—
390	C₂×D₂₆₉	C₂²×D₄	1	4	yes	—
391	C₂×D₂₆₉	H(5,𝔽₂)	1	2	yes	complemented
392	C₄×C₂₆₉	—	2	1	no	—
393	C₄×C₂₆₉	—	2	1	no	—
394	C₄×C₂₆₉	—	2	2	no	—
395	C₄×C₂₆₉	—	2	1	no	—
396	C₄×C₂₆₉	—	2	2	no	—
397	C₄×C₂₆₉	—	2	1	no	—
398	C₄×C₂₆₉	C₂²×D₄	1	2	yes	—
399	Dic₂₆₉	—	2	1	no	—
400	Dic₂₆₉	—	2	1	no	—
401	Dic₂₆₉	—	2	1	no	—
402	Dic₂₆₉	—	2	2	no	—
403	Dic₂₆₉	—	2	1	no	—
404	Dic₂₆₉	C₂²×D₄	1	2	yes	—
405	C₂×C₂₆₉	—	2	2	no	—
406	C₂×C₂₆₉	—	2	4	no	—
407	C₂×C₂₆₉	—	4	2	no	—
408	C₂×C₂₆₉	—	4	1	no	—
409	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
410	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
412	D₂₆₉	—	2	2	no	—
413	D₂₆₉	—	2	2	no	—
414	D₂₆₉	—	2	4	no	—
415	D₂₆₉	—	4	2	no	—
416	D₂₆₉	—	4	1	no	—
417	D₂₆₉	—	4	2	no	—
418	C₂₆₉	#3484	1	1	yes	characteristic, complemented, Sylow
419	#3484	—	269	1	no	maximal, Sylow
420	C₂×H(5,𝔽₂)	—	269	1	no	—
421	C₂³×D₄	—	269	1	no	—
422	#546	—	269	1	no	—
423	#546	—	269	1	no	—
424	#546	—	269	2	no	—
425	#546	—	269	1	no	—
426	#546	—	269	2	no	—
427	#546	D₂₆₉	1	1	yes	characteristic, complemented
428	D₄²	—	269	1	no	—
429	D₄²	—	269	2	no	—
430	D₄²	—	269	1	no	—
431	D₄²	—	269	2	no	—
432	D₄²	—	269	1	no	—
433	D₄²	—	269	1	no	—
434	#535	—	269	1	no	—
435	#535	—	269	1	no	—
436	#534	—	269	2	no	—
437	#534	—	269	2	no	—
438	#525	—	269	1	no	—
439	#525	—	269	1	no	—
440	C₂×#120	—	269	2	no	—
441	C₂×#120	—	269	2	no	—
442	#518	—	269	1	no	—
443	C₂⁵	—	269	2	no	—
444	H(5,𝔽₂)	—	538	8	no	—
445	C₂×#41	—	269	1	no	—
446	C₂×#41	—	269	1	no	—
447	C₂×#41	—	269	1	no	—
448	C₂×#41	—	269	2	no	—
449	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic, complemented
450	C₂²×D₄	—	269	1	no	—
451	C₂²×D₄	—	269	2	no	—
452	C₂²×D₄	—	269	2	no	—
453	C₂²×D₄	—	269	2	no	—
454	C₂²×D₄	—	269	1	no	—
455	C₂²×D₄	—	269	1	no	—
456	C₂²×D₄	—	269	2	no	—
457	C₂²×D₄	—	269	1	no	—
458	C₂²×D₄	—	269	1	no	—
459	C₂²×D₄	—	269	2	no	—
460	C₂²×D₄	—	269	2	no	—
461	C₂²×D₄	—	269	2	no	—
462	C₂²×D₄	—	269	2	no	—
463	C₂²×D₄	—	269	1	no	—
464	C₂²×D₄	—	269	2	no	—
465	C₂²×D₄	—	269	1	no	—
466	C₂²×D₄	—	269	2	no	—
467	C₂²×D₄	—	538	8	no	—
468	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
469	C₂³×C₄	—	269	1	no	—
470	#127	—	269	1	no	—
471	#127	—	269	2	no	—
472	#127	—	269	1	no	—
473	#124	—	269	1	no	—
474	#124	—	269	2	no	—
475	#124	C₂×D₂₆₉	1	1	yes	characteristic, complemented
476	#123	—	269	2	no	—
477	#123	—	269	2	no	—
478	#123	—	269	1	no	—
479	#123	—	269	2	no	—
480	#123	—	269	1	no	—
481	#123	—	269	2	no	—
482	#123	C₂×D₂₆₉	1	2	yes	complemented
483	C₂²⋊Q₈	—	269	1	no	—
484	C₂²⋊Q₈	—	269	1	no	—
485	C₂²⋊Q₈	—	269	1	no	—
486	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
487	#121	—	269	1	no	—
488	#121	—	269	2	no	—
489	#121	—	269	1	no	—
490	#121	—	269	2	no	—
491	#121	—	269	1	no	—
492	#121	—	269	2	no	—
493	#121	—	269	1	no	—
494	#121	—	269	1	no	—
495	#121	—	269	2	no	—
496	#121	—	269	2	no	—
497	#121	—	269	1	no	—
498	#121	—	269	1	no	—
499	#121	—	269	2	no	—
500	#121	—	269	2	no	—
501	#121	—	269	2	no	—
502	#121	—	269	2	no	—
503	#121	C₂×D₂₆₉	1	2	yes	complemented
504	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
505	#120	—	269	2	no	—
506	#120	—	269	1	no	—
507	#120	—	269	2	no	—
508	#120	—	269	2	no	—
509	#120	—	269	2	no	—
510	#120	—	269	2	no	—
511	#120	—	269	2	no	—
512	#120	—	269	1	no	—
513	#120	—	269	2	no	—
514	#120	—	269	2	no	—
515	#120	—	269	2	no	—
516	#120	—	269	2	no	—
517	#120	—	269	2	no	—
518	#120	—	269	2	no	—
519	#120	—	269	2	no	—
520	#120	—	269	2	no	—
521	#120	—	269	2	no	—
522	#120	—	269	2	no	—
523	#120	C₂×D₂₆₉	1	2	yes	complemented
524	C₄×D₄	—	269	1	no	—
525	C₄×D₄	—	269	1	no	—
526	C₄×D₄	—	269	2	no	—
527	C₄×D₄	—	269	1	no	—
528	C₄×D₄	—	269	1	no	—
529	C₄×D₄	—	269	2	no	—
530	C₄×D₄	—	269	2	no	—
531	C₄×D₄	—	269	2	no	—
532	C₄×D₄	—	269	1	no	—
533	C₄×D₄	—	269	1	no	—
534	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
535	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
536	#117	—	269	1	no	—
537	#117	—	269	1	no	—
538	C₂×C₂²⋊C₄	—	269	2	no	—
539	C₂×C₂²⋊C₄	—	269	2	no	—
540	C₂×C₂²⋊C₄	—	269	2	no	—
541	C₂×C₂²⋊C₄	—	269	2	no	—
542	C₂×C₂²⋊C₄	—	269	2	no	—
543	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
544	C₂⁴	—	269	2	no	—
545	C₂⁴	—	269	1	no	—
546	C₂⁴	—	269	2	no	—
547	C₂⁴	—	269	2	no	—
548	C₂⁴	—	269	2	no	—
549	C₂⁴	—	269	2	no	—
550	C₂⁴	—	269	2	no	—
551	C₂⁴	—	269	2	no	—
552	C₂⁴	—	538	8	no	—
553	C₂⁴	—	1076	4	no	—
554	C₂⁴	—	1076	4	no	—
555	C₂⁴	C₂²×D₂₆₉	1	2	yes	—
556	#41	—	2	4	no	—
557	#41	—	538	4	no	—
558	#41	—	538	8	no	—
559	#41	—	538	4	no	—
560	#41	—	538	4	no	—
561	C₂×Q₈	—	269	1	no	—
562	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	269	2	no	—
565	C₂×D₄	—	269	8	no	—
566	C₂×D₄	—	269	1	no	—
567	C₂×D₄	—	269	1	no	—
568	C₂×D₄	—	269	2	no	—
569	C₂×D₄	—	269	1	no	—
570	C₂×D₄	—	269	2	no	—
571	C₂×D₄	—	269	2	no	—
572	C₂×D₄	—	269	2	no	—
573	C₂×D₄	—	269	2	no	—
574	C₂×D₄	—	269	1	no	—
575	C₂×D₄	—	269	2	no	—
576	C₂×D₄	—	269	2	no	—
577	C₂×D₄	—	269	2	no	—
578	C₂×D₄	—	269	2	no	—
579	C₂×D₄	—	269	1	no	—
580	C₂×D₄	—	269	2	no	—
581	C₂×D₄	—	269	1	no	—
582	C₂×D₄	—	269	2	no	—
583	C₂×D₄	—	269	1	no	—
584	C₂×D₄	—	269	2	no	—
585	C₂×D₄	—	269	2	no	—
586	C₂×D₄	—	269	2	no	—
587	C₂×D₄	—	269	1	no	—
588	C₂×D₄	—	269	1	no	—
589	C₂×D₄	—	269	2	no	—
590	C₂×D₄	—	269	2	no	—
591	C₂×D₄	—	269	2	no	—
592	C₂×D₄	—	538	4	no	—
593	C₂×D₄	—	538	4	no	—
594	C₂×D₄	—	538	8	no	—
595	C₂×D₄	—	538	4	no	—
596	C₂×D₄	—	538	8	no	—
597	C₂×D₄	—	538	4	no	—
598	C₂×D₄	—	538	8	no	—
599	C₂×D₄	—	538	8	no	—
600	C₂×D₄	—	538	8	no	—
601	C₂×D₄	—	538	8	no	—
602	C₂×D₄	—	538	4	no	—
603	C₂×D₄	—	538	4	no	—
604	C₂×D₄	—	1076	4	no	—
605	C₂×D₄	—	1076	4	no	—
606	C₂×D₄	—	1076	4	no	—
607	C₂×D₄	—	1076	4	no	—
608	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
609	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
610	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
611	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
612	C₂×D₄	C₂²×D₂₆₉	1	2	yes	complemented
613	C₂×D₄	C₂²×D₂₆₉	1	2	yes	complemented
614	C₂²×C₄	—	269	1	no	—
615	C₂²×C₄	—	269	1	no	—
616	C₂²×C₄	—	269	2	no	—
617	C₂²×C₄	—	269	2	no	—
618	C₂²×C₄	—	269	2	no	—
619	C₂²×C₄	—	269	1	no	—
620	C₂²×C₄	—	269	1	no	—
621	C₂²×C₄	—	269	1	no	—
622	C₂²×C₄	—	269	1	no	—
623	C₂²×C₄	—	269	2	no	—
624	C₂²×C₄	—	269	2	no	—
625	C₂²×C₄	—	538	4	no	—
626	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
627	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	complemented
628	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
629	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	complemented
630	C₄⋊C₄	—	269	1	no	—
631	C₄⋊C₄	—	269	1	no	—
632	C₄⋊C₄	—	269	1	no	—
633	C₄⋊C₄	—	269	1	no	—
634	C₄⋊C₄	—	269	2	no	—
635	C₄⋊C₄	—	269	1	no	—
636	C₄⋊C₄	—	269	1	no	—
637	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
638	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
639	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
640	C₂²⋊C₄	—	269	1	no	—
641	C₂²⋊C₄	—	269	2	no	—
642	C₂²⋊C₄	—	269	2	no	—
643	C₂²⋊C₄	—	269	1	no	—
644	C₂²⋊C₄	—	269	2	no	—
645	C₂²⋊C₄	—	269	1	no	—
646	C₂²⋊C₄	—	269	1	no	—
647	C₂²⋊C₄	—	269	2	no	—
648	C₂²⋊C₄	—	269	1	no	—
649	C₂²⋊C₄	—	269	1	no	—
650	C₂²⋊C₄	—	269	2	no	—
651	C₂²⋊C₄	—	269	2	no	—
652	C₂²⋊C₄	—	269	2	no	—
653	C₂²⋊C₄	—	269	2	no	—
654	C₂²⋊C₄	—	269	2	no	—
655	C₂²⋊C₄	—	269	2	no	—
656	C₂²⋊C₄	—	269	1	no	—
657	C₂²⋊C₄	—	269	2	no	—
658	C₂²⋊C₄	—	269	2	no	—
659	C₂²⋊C₄	—	269	1	no	—
660	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
661	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
662	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
663	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
664	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
665	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
666	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
667	C₄²	—	269	2	no	—
668	C₄²	—	269	1	no	—
669	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	269	1	no	—
674	C₂³	—	269	1	no	—
675	C₂³	—	269	2	no	—
676	C₂³	—	269	8	no	—
677	C₂³	—	269	2	no	—
678	C₂³	—	269	2	no	—
679	C₂³	—	269	1	no	—
680	C₂³	—	538	2	no	—
681	C₂³	—	538	2	no	—
682	C₂³	—	538	4	no	—
683	C₂³	—	538	4	no	—
684	C₂³	—	538	4	no	—
685	C₂³	—	538	4	no	—
686	C₂³	—	538	4	no	—
687	C₂³	—	538	4	no	—
688	C₂³	—	538	2	no	—
689	C₂³	—	538	4	no	—
690	C₂³	—	538	4	no	—
691	C₂³	—	538	4	no	—
692	C₂³	—	1076	2	no	—
693	C₂³	—	1076	2	no	—
694	C₂³	—	1076	2	no	—
695	C₂³	—	1076	2	no	—
696	C₂³	—	1076	2	no	—
697	C₂³	—	1076	2	no	—
698	C₂³	—	1076	2	no	—
699	C₂³	—	1076	2	no	—
700	C₂³	—	1076	2	no	—
701	C₂³	—	1076	2	no	—
702	C₂³	—	1076	2	no	—
703	C₂³	—	1076	32	no	—
704	C₂³	C₂³×D₂₆₉	1	2	yes	—
705	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
706	C₂³	C₂³×D₂₆₉	1	2	yes	—
707	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
708	Q₈	—	2	2	no	—
709	Q₈	—	538	2	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	4	2	no	—
715	D₄	—	269	8	no	—
716	D₄	—	269	4	no	—
717	D₄	—	538	4	no	—
718	D₄	—	538	2	no	—
719	D₄	—	538	4	no	—
720	D₄	—	538	4	no	—
721	D₄	—	538	4	no	—
722	D₄	—	538	2	no	—
723	D₄	—	538	4	no	—
724	D₄	—	538	4	no	—
725	D₄	—	538	2	no	—
726	D₄	—	538	4	no	—
727	D₄	—	538	2	no	—
728	D₄	—	538	2	no	—
729	D₄	—	538	4	no	—
730	D₄	—	538	4	no	—
731	D₄	—	538	4	no	—
732	D₄	—	538	2	no	—
733	D₄	—	538	2	no	—
734	D₄	—	538	2	no	—
735	D₄	—	1076	2	no	—
736	D₄	—	1076	2	no	—
737	D₄	—	1076	2	no	—
738	D₄	—	1076	2	no	—
739	D₄	—	1076	2	no	—
740	D₄	—	1076	2	no	—
741	D₄	—	1076	2	no	—
742	D₄	D₄×D₂₆₉	1	4	yes	complemented
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	269	1	no	—
748	C₂×C₄	—	269	4	no	—
749	C₂×C₄	—	269	1	no	—
750	C₂×C₄	—	269	2	no	—
751	C₂×C₄	—	269	1	no	—
752	C₂×C₄	—	269	1	no	—
753	C₂×C₄	—	269	1	no	—
754	C₂×C₄	—	538	2	no	—
755	C₂×C₄	—	538	4	no	—
756	C₂×C₄	—	538	2	no	—
757	C₂×C₄	—	538	4	no	—
758	C₂×C₄	—	538	2	no	—
759	C₂×C₄	—	538	2	no	—
760	C₂×C₄	—	538	2	no	—
761	C₂×C₄	—	1076	2	no	—
762	C₂×C₄	—	1076	2	no	—
763	C₂×C₄	—	1076	2	no	—
764	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
765	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
766	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
767	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
768	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
769	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
770	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
771	C₂²	—	2	1	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	4	8	no	—
782	C₂²	—	269	2	no	—
783	C₂²	—	269	4	no	—
784	C₂²	—	269	2	no	—
785	C₂²	—	538	8	no	—
786	C₂²	—	538	1	no	—
787	C₂²	—	538	2	no	—
788	C₂²	—	538	1	no	—
789	C₂²	—	538	2	no	—
790	C₂²	—	538	1	no	—
791	C₂²	—	538	1	no	—
792	C₂²	—	538	2	no	—
793	C₂²	—	538	1	no	—
794	C₂²	—	538	2	no	—
795	C₂²	—	538	1	no	—
796	C₂²	—	538	2	no	—
797	C₂²	—	538	2	no	—
798	C₂²	—	538	2	no	—
799	C₂²	—	538	1	no	—
800	C₂²	—	538	2	no	—
801	C₂²	—	1076	8	no	—
802	C₂²	—	1076	8	no	—
803	C₂²	—	1076	8	no	—
804	C₂²	—	1076	8	no	—
805	C₂²	—	1076	8	no	—
806	C₂²	—	2152	4	no	—
807	C₂²	—	2152	4	no	—
808	C₂²	C₂×D₄×D₂₆₉	1	4	yes	—
809	C₂²	#22575499	1	2	yes	complemented
810	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	1	no	—
817	C₄	—	269	2	no	—
818	C₄	—	538	1	no	—
819	C₄	—	538	1	no	—
820	C₄	—	538	1	no	—
821	C₄	—	538	2	no	—
822	C₄	—	538	1	no	—
823	C₄	C₂×D₄×D₂₆₉	1	2	yes	—
824	C₂	—	2	2	no	—
825	C₂	—	2	4	no	—
826	C₂	—	4	2	no	—
827	C₂	—	4	1	no	—
828	C₂	—	538	2	no	—
829	C₂	—	538	2	no	—
830	C₂	—	538	4	no	—
831	C₂	—	1076	2	no	—
832	C₂	—	1076	1	no	—
833	C₂	—	1076	2	no	—
834	C₂	C₂²×D₄×D₂₆₉	1	1	yes	characteristic
835	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
836	C₂	C₂×#22575499	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#546×C₂₆₉	C₂
hypercenter	#546	D₂₆₉
hypocenter	C₂₆₉	#3484
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#22575499	C₂	semidirect
2. C₂²×D₄×D₂₆₉	C₂	semidirect
3. #31771248	C₂	semidirect
4. #31771247	C₂	semidirect
5. #31771246	C₂	semidirect
6. #31771245	C₂	semidirect
7. #31771243	C₂	semidirect
8. D₄×D₁₀₇₆	C₂	semidirect
9. D₄×D₁₀₇₆	C₂	semidirect
10. #31771239	C₂	semidirect
11. #31771239	C₂	semidirect
12. D₄×C₂²⋊D₂₆₉	C₂	semidirect
13. #31771237	C₂	semidirect
14. #31771173	C₂	semidirect
15. #31771171	C₂	semidirect
16. #31771166	C₂	semidirect
17. #31771163	C₂	semidirect
18. #31771118	C₂	semidirect
19. #31771114	C₂	semidirect
20. C₂×#22575423	C₂	semidirect
21. #120×D₂₆₉	C₂	semidirect
22. #31771077	C₂	semidirect
23. #546×C₂₆₉	C₂	semidirect
24. C₂⁴×D₂₆₉	C₂²	semidirect
26. C₂×#16864403	C₂²	semidirect
27. C₂×#16864403	C₂²	semidirect
28. C₂×#16864402	C₂²	semidirect
29. C₂×#16864402	C₂²	semidirect
30. C₂²×D₁₀₇₆	C₂²	semidirect
31. C₂²×D₁₀₇₆	C₂²	semidirect
32. C₂²×D₁₀₇₆	C₂²	semidirect
33. C₂²×D₁₀₇₆	C₂²	semidirect
34. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
35. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
38. C₂×D₄×D₂₆₉	C₂²	semidirect
39. C₂×D₄×D₂₆₉	C₂²	semidirect
40. C₂×D₄×D₂₆₉	C₂²	semidirect
41. C₂×D₄×D₂₆₉	C₂²	semidirect
42. C₂×D₄×D₂₆₉	C₂²	semidirect
43. C₂×D₄×D₂₆₉	C₂²	semidirect
44. C₂×D₄×D₂₆₉	C₂²	semidirect
45. C₂×D₄×D₂₆₉	C₂²	semidirect
46. C₂×D₄×D₂₆₉	C₂²	semidirect
47. C₂×D₄×D₂₆₉	C₂²	semidirect
48. C₂²×C₄×D₂₆₉	C₂²	semidirect
49. #22575450	C₂²	semidirect
50. #22575449	C₂²	semidirect
51. #22575449	C₂²	semidirect
52. #22575442	C₂²	semidirect
53. #22575439	C₂²	semidirect
54. #22575438	C₂²	semidirect
55. #22575438	C₂²	semidirect
56. #22575438	C₂²	semidirect
57. #22575436	C₂²	semidirect
58. #22575435	C₂²	semidirect
59. #22575435	C₂²	semidirect
60. #22575431	C₂²	semidirect
61. #22575430	C₂²	semidirect
62. #22575429	C₂²	semidirect
63. #22575428	C₂²	semidirect
64. #22575428	C₂²	semidirect
65. #22575428	C₂²	semidirect
66. #22575428	C₂²	semidirect
67. #22575427	C₂²	semidirect
68. #22575427	C₂²	semidirect
69. #22575427	C₂²	semidirect
70. #22575426	C₂²	semidirect
71. #22575426	C₂²	semidirect
72. #22575426	C₂²	semidirect
73. #22575426	C₂²	semidirect
74. #22575426	C₂²	semidirect
75. #22575425	C₂²	semidirect
76. #22575425	C₂²	semidirect
77. #22575425	C₂²	semidirect
78. #22575424	C₂²	semidirect
79. #22575423	C₂²	semidirect
80. #22575423	C₂²	semidirect
81. #22575423	C₂²	semidirect
82. #22575423	C₂²	semidirect
83. #22575423	C₂²	semidirect
84. #22575423	C₂²	semidirect
85. #22575423	C₂²	semidirect
86. #22575423	C₂²	semidirect
87. #22575423	C₂²	semidirect
88. #22575423	C₂²	semidirect
89. #22575423	C₂²	semidirect
90. #22575423	C₂²	semidirect
91. #22575422	C₂²	semidirect
92. #22575421	C₂²	semidirect
93. #22575421	C₂²	semidirect
94. #22575421	C₂²	semidirect
95. #22575421	C₂²	semidirect
96. #22575421	C₂²	semidirect
97. C₄×D₁₀₇₆	C₂²	semidirect
98. C₄×D₁₀₇₆	C₂²	semidirect
99. D₄×Dic₂₆₉	C₂²	semidirect
100. #22575415	C₂²	semidirect
101. #22575415	C₂²	semidirect
102. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
103. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
104. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
105. #22575413	C₂²	semidirect
106. #22575413	C₂²	semidirect
107. #22575411	C₂²	semidirect
108. #22575410	C₂²	semidirect
109. C₂×#16864379	C₂²	semidirect
110. C₂×#16864379	C₂²	semidirect
111. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
112. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
113. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
114. C₂×#41×C₂₆₉	C₂²	semidirect
115. C₂²×D₄×C₂₆₉	C₂²	semidirect
116. #124×C₂₆₉	C₂²	semidirect
117. #123×C₂₆₉	C₂²	semidirect
118. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
119. #121×C₂₆₉	C₂²	semidirect
120. #121×C₂₆₉	C₂²	semidirect
121. #120×C₂₆₉	C₂²	semidirect
122. C₄×D₄×C₂₆₉	C₂²	semidirect
123. C₄×D₄×C₂₆₉	C₂²	semidirect
124. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
134. C₂³×D₂₆₉	C₂³	semidirect
135. C₂³×D₂₆₉	C₂³	semidirect
140. C₂×Dic₅₃₈	C₂³	semidirect
152. C₂×D₁₀₇₆	C₂³	semidirect
153. C₂×D₁₀₇₆	C₂³	semidirect
154. C₂×D₁₀₇₆	C₂³	semidirect
155. C₂×D₁₀₇₆	C₂³	semidirect
156. C₂×D₁₀₇₆	C₂³	semidirect
157. C₂×D₁₀₇₆	C₂³	semidirect
168. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
169. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
170. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
171. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
172. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
173. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
184. D₄×D₂₆₉	D₄	semidirect
186. C₂²×Dic₂₆₉	C₂³	semidirect
192. C₂×C₄×D₂₆₉	C₂³	semidirect
193. C₂×C₄×D₂₆₉	C₂³	semidirect
194. C₂×C₄×D₂₆₉	C₂³	semidirect
195. C₂×C₄×D₂₆₉	C₂³	semidirect
196. C₂×C₄×D₂₆₉	C₂³	semidirect
197. C₄⋊Dic₂₆₉	C₂³	semidirect
198. C₄⋊Dic₂₆₉	C₂³	semidirect
199. #16864381	C₂³	semidirect
200. #16864381	C₂³	semidirect
201. #16864381	C₂³	semidirect
202. #16864381	C₂³	semidirect
203. #16864381	C₂³	semidirect
205. C₂²⋊Dic₂₆₉	C₂³	semidirect
206. C₂²⋊Dic₂₆₉	C₂³	semidirect
207. C₂²⋊Dic₂₆₉	C₂³	semidirect
214. #16864379	C₂³	semidirect
215. #16864379	C₂³	semidirect
216. #16864379	C₂³	semidirect
217. #16864379	C₂³	semidirect
218. #16864379	C₂³	semidirect
219. #16864379	C₂³	semidirect
220. #16864379	C₂³	semidirect
221. #16864379	C₂³	semidirect
222. #16864379	C₂³	semidirect
223. #16864379	C₂³	semidirect
224. C₄×Dic₂₆₉	C₂³	semidirect
225. C₄×Dic₂₆₉	C₂³	semidirect
228. C₂×Q₈×C₂₆₉	C₂³	semidirect
234. C₂×D₄×C₂₆₉	C₂³	semidirect
235. C₂×D₄×C₂₆₉	C₂³	semidirect
237. C₂²×C₄×C₂₆₉	C₂³	semidirect
238. C₂²×C₄×C₂₆₉	C₂³	semidirect
239. C₂²×C₄×C₂₆₉	C₂³	semidirect
240. C₄⋊C₄×C₂₆₉	C₂³	semidirect
241. C₄⋊C₄×C₂₆₉	C₂³	semidirect
242. C₄⋊C₄×C₂₆₉	C₂³	semidirect
245. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
246. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
247. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
248. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
249. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
250. C₄²×C₂₆₉	C₂³	semidirect
275. C₂²×D₂₆₉	C₂×D₄	semidirect
295. D₁₀₇₆	C₂×D₄	semidirect
309. C₂²⋊D₂₆₉	C₂×D₄	semidirect
326. C₄×D₂₆₉	C₂×D₄	semidirect
340. D₄×C₂₆₉	C₂×D₄	semidirect
364. C₂²×C₂₆₉	H(5,𝔽₂)	semidirect
391. C₂×D₂₆₉	H(5,𝔽₂)	semidirect
418. C₂₆₉	#3484	semidirect
427. #546	D₂₆₉	semidirect
449. C₂×#41	C₂×D₂₆₉	semidirect
468. C₂²×D₄	C₂×D₂₆₉	semidirect
475. #124	C₂×D₂₆₉	semidirect
482. #123	C₂×D₂₆₉	semidirect
486. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
503. #121	C₂×D₂₆₉	semidirect
504. #121	C₂×D₂₆₉	semidirect
523. #120	C₂×D₂₆₉	semidirect
534. C₄×D₄	C₂×D₂₆₉	semidirect
535. C₄×D₄	C₂×D₂₆₉	semidirect
543. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
562. C₂×Q₈	C₂²×D₂₆₉	semidirect
612. C₂×D₄	C₂²×D₂₆₉	semidirect
613. C₂×D₄	C₂²×D₂₆₉	semidirect
627. C₂²×C₄	C₂²×D₂₆₉	semidirect
628. C₂²×C₄	C₂²×D₂₆₉	semidirect
629. C₂²×C₄	C₂²×D₂₆₉	semidirect
637. C₄⋊C₄	C₂²×D₂₆₉	semidirect
638. C₄⋊C₄	C₂²×D₂₆₉	semidirect
639. C₄⋊C₄	C₂²×D₂₆₉	semidirect
662. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
663. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
664. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
665. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
666. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
669. C₄²	C₂²×D₂₆₉	semidirect
742. D₄	D₄×D₂₆₉	semidirect
809. C₂²	#22575499	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22575499	2
C₂²×D₄×D₂₆₉	2
#31771248	2
#31771247	2
#31771246	2
#31771245	2
#31771243	2
D₄×D₁₀₇₆	2
#31771239	2
D₄×C₂²⋊D₂₆₉	2
#31771237	2
#31771173	2
#31771171	2
#31771166	2
#31771163	2
#31771118	2
#31771114	2
C₂×#22575423	2
#120×D₂₆₉	2
#31771077	2
#546×C₂₆₉	2
#3484	269