Subgroups — #46824924

Order 34432.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771327	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771315	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771310	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771288	C₂	1	2	yes	maximal, complemented
5	#31771284	C₂	1	2	yes	maximal, complemented
6	#31771279	C₂	1	2	yes	maximal, complemented
7	D₄×Dic₅₃₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771264	C₂	1	2	yes	maximal, complemented
9	#31771256	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771254	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771250	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771243	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771227	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771226	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771202	C₂	1	2	yes	maximal, complemented
16	#31771197	C₂	1	2	yes	maximal, complemented
17	#31771159	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771133	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771114	C₂	1	2	yes	maximal, complemented
20	C₂×#22575431	C₂	1	2	yes	maximal, complemented
21	#31771084	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#520×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16864402	C₂²	1	2	yes	complemented
25	C₂×#16864401	C₂²	1	1	yes	characteristic
26	C₂²×Dic₅₃₈	C₂²	1	2	yes	complemented
27	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	—
29	#22575453	C₂²	1	1	yes	characteristic, complemented
30	#22575452	C₂²	1	1	yes	characteristic, complemented
31	#22575452	C₂²	1	1	yes	characteristic, complemented
32	#22575451	C₂²	1	1	yes	characteristic, complemented
33	#22575448	C₂²	1	1	yes	characteristic, complemented
34	#22575448	C₂²	1	2	yes	complemented
35	#22575448	C₂²	1	2	yes	complemented
36	#22575447	C₂²	1	2	yes	complemented
37	#22575447	C₂²	1	2	yes	complemented
38	#22575446	C₂²	1	1	yes	characteristic, complemented
39	#22575445	C₂²	1	2	yes	complemented
40	#22575443	C₂²	1	2	yes	complemented
41	#22575443	C₂²	1	2	yes	complemented
42	#22575443	C₂²	1	1	yes	characteristic, complemented
43	#22575442	C₂²	1	1	yes	characteristic
44	#22575441	C₂²	1	1	yes	characteristic
45	#22575441	C₂²	1	2	yes	complemented
46	#22575439	C₂²	1	2	yes	complemented
47	#22575439	C₂²	1	1	yes	characteristic, complemented
48	#22575438	C₂²	1	1	yes	characteristic
49	#22575438	C₂²	1	2	yes	complemented
50	#22575438	C₂²	1	2	yes	complemented
51	#22575437	C₂²	1	2	yes	—
52	#22575436	C₂²	1	2	yes	—
53	#22575436	C₂²	1	2	yes	complemented
54	#22575436	C₂²	1	2	yes	complemented
55	#22575435	C₂²	1	1	yes	characteristic
56	#22575435	C₂²	1	2	yes	complemented
57	#22575434	C₂²	1	2	yes	complemented
58	#22575433	C₂²	1	1	yes	characteristic
59	#22575432	C₂²	1	2	yes	complemented
60	#22575432	C₂²	1	2	yes	complemented
61	#22575432	C₂²	1	1	yes	characteristic, complemented
62	#22575431	C₂²	1	2	yes	—
63	#22575431	C₂²	1	2	yes	—
64	#22575431	C₂²	1	2	yes	—
65	#22575431	C₂²	1	1	yes	characteristic
66	#22575431	C₂²	1	2	yes	complemented
67	#22575431	C₂²	1	2	yes	complemented
68	#22575431	C₂²	1	2	yes	complemented
69	#22575431	C₂²	1	2	yes	complemented
70	#22575431	C₂²	1	2	yes	complemented
71	#22575430	C₂²	1	2	yes	complemented
72	#22575430	C₂²	1	2	yes	complemented
73	#22575429	C₂²	1	1	yes	characteristic
74	#22575429	C₂²	1	1	yes	characteristic, complemented
75	#22575428	C₂²	1	1	yes	characteristic
76	#22575427	C₂²	1	2	yes	—
77	#22575427	C₂²	1	1	yes	characteristic
78	#22575426	C₂²	1	1	yes	characteristic
79	#22575425	C₂²	1	2	yes	—
80	#22575425	C₂²	1	2	yes	complemented
81	#22575423	C₂²	1	2	yes	—
82	#22575421	C₂²	1	2	yes	—
83	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
84	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
85	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
86	#22575418	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
88	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
89	C₄×D₁₀₇₆	C₂²	1	2	yes	—
90	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
91	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
92	#22575415	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
98	#22575413	C₂²	1	2	yes	—
99	#22575413	C₂²	1	2	yes	complemented
100	#22575410	C₂²	1	2	yes	—
101	#22575410	C₂²	1	1	yes	characteristic, complemented
102	#22575410	C₂²	1	2	yes	complemented
103	#22575409	C₂²	1	2	yes	complemented
104	C₂×#16864381	C₂²	1	2	yes	complemented
105	C₂×#16864381	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
108	C₂×#16864379	C₂²	1	2	yes	—
109	C₂×#16864379	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
111	C₄²×D₂₆₉	C₂²	1	1	yes	characteristic
112	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic
113	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
116	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
118	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
119	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
120	#117×C₂₆₉	C₂²	1	2	yes	complemented
121	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₆₉	C₂³	1	2	yes	—
124	#16864402	—	4	4	no	—
125	#16864401	—	2	4	no	—
126	C₂×Dic₅₃₈	—	4	4	no	—
127	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₅₃₈	C₂³	1	2	yes	—
129	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₅₃₈	C₂³	1	2	yes	—
131	C₂×Dic₅₃₈	C₂³	1	2	yes	—
132	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
133	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
134	C₂×D₁₀₇₆	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
140	D₄×D₂₆₉	—	2	4	no	—
141	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
142	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
143	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
144	C₂×C₄×D₂₆₉	—	4	4	no	—
145	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
150	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
151	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
152	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
153	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
156	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
158	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
159	#16864381	C₂³	1	2	yes	—
160	#16864381	C₂³	1	2	yes	—
161	#16864381	C₂³	1	1	yes	characteristic
162	#16864381	C₂³	1	1	yes	characteristic
163	#16864381	C₂³	1	2	yes	—
164	#16864381	C₂³	1	2	yes	—
165	#16864381	C₂³	1	2	yes	—
166	#16864381	C₂³	1	2	yes	—
167	#16864381	C₂³	1	2	yes	—
168	#16864381	C₂³	1	1	yes	characteristic
169	#16864381	C₂³	1	2	yes	—
170	#16864381	C₂³	1	2	yes	—
171	#16864381	C₂³	1	1	yes	characteristic
172	#16864381	C₂³	1	2	yes	—
173	#16864381	C₂³	1	1	yes	characteristic
174	#16864381	C₂³	1	2	yes	—
175	#16864381	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
181	#16864379	C₂³	1	2	yes	—
182	#16864379	C₂³	1	2	yes	—
183	#16864379	C₂³	1	1	yes	characteristic
184	#16864379	C₂³	1	1	yes	characteristic
185	#16864379	C₂³	1	2	yes	—
186	#16864379	C₂³	1	2	yes	—
187	#16864379	C₂³	1	2	yes	—
188	#16864379	C₂³	1	2	yes	—
189	#16864379	C₂³	1	2	yes	—
190	#16864379	C₂³	1	2	yes	—
191	#16864379	C₂³	1	1	yes	characteristic
192	#16864379	C₂³	1	1	yes	characteristic
193	#16864379	C₂³	1	2	yes	—
194	#16864379	C₂³	1	2	yes	—
195	#16864379	C₂³	1	1	yes	characteristic
196	#16864379	C₂³	1	2	yes	—
197	#16864379	C₂³	1	1	yes	characteristic
198	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₆₉	C₂³	1	2	yes	—
202	C₄×Dic₂₆₉	C₂³	1	2	yes	—
203	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
204	#41×C₂₆₉	—	2	4	no	—
205	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
207	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
209	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
211	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
212	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
224	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
225	C₄²×C₂₆₉	C₂³	1	2	yes	—
226	C₄²×C₂₆₉	C₂³	1	2	yes	—
227	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
228	C₂²×D₂₆₉	—	2	4	no	—
229	C₂²×D₂₆₉	—	2	4	no	—
230	C₂²×D₂₆₉	—	4	2	no	—
231	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
232	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
233	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
234	Dic₅₃₈	—	2	2	no	—
235	Dic₅₃₈	—	2	2	no	—
236	Dic₅₃₈	—	2	4	no	—
237	Dic₅₃₈	—	4	2	no	—
238	Dic₅₃₈	—	4	2	no	—
239	D₁₀₇₆	—	2	2	no	—
240	D₁₀₇₆	—	2	2	no	—
241	D₁₀₇₆	—	4	2	no	—
242	C₂²⋊D₂₆₉	—	2	4	no	—
243	C₂²⋊D₂₆₉	—	2	4	no	—
244	C₂²⋊D₂₆₉	—	2	2	no	—
245	C₂²⋊D₂₆₉	—	2	2	no	—
246	C₂²⋊D₂₆₉	—	4	2	no	—
247	C₂×Dic₂₆₉	—	2	4	no	—
248	C₂×Dic₂₆₉	—	2	4	no	—
249	C₂×Dic₂₆₉	—	4	2	no	—
250	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
253	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
256	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
258	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
259	C₄×D₂₆₉	—	2	2	no	—
260	C₄×D₂₆₉	—	2	2	no	—
261	C₄×D₂₆₉	—	2	2	no	—
262	C₄×D₂₆₉	—	2	2	no	—
263	C₄×D₂₆₉	—	2	4	no	—
264	C₄×D₂₆₉	—	4	2	no	—
265	C₄×D₂₆₉	—	4	2	no	—
266	C₄×D₂₆₉	—	4	2	no	—
267	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
268	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
269	Q₈×C₂₆₉	—	2	2	no	—
270	D₄×C₂₆₉	—	2	4	no	—
271	D₄×C₂₆₉	#41	1	4	yes	complemented
272	C₂×C₄×C₂₆₉	—	2	4	no	—
273	C₂×C₄×C₂₆₉	—	2	2	no	—
274	C₂×C₄×C₂₆₉	—	4	2	no	—
275	C₂×C₄×C₂₆₉	—	4	2	no	—
276	C₂×C₄×C₂₆₉	—	4	2	no	—
277	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
280	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
282	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
284	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₂₆₉	—	2	2	no	—
287	C₂²×C₂₆₉	—	2	2	no	—
288	C₂²×C₂₆₉	—	2	1	no	—
289	C₂²×C₂₆₉	—	2	1	no	—
290	C₂²×C₂₆₉	—	2	1	no	—
291	C₂²×C₂₆₉	C₂×#41	1	4	yes	—
292	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
293	C₂×D₂₆₉	—	2	1	no	—
294	C₂×D₂₆₉	—	2	1	no	—
295	C₂×D₂₆₉	—	2	1	no	—
296	C₂×D₂₆₉	—	2	2	no	—
297	C₂×D₂₆₉	—	2	2	no	—
298	C₂×D₂₆₉	—	2	1	no	—
299	C₂×D₂₆₉	—	2	1	no	—
300	C₂×D₂₆₉	—	2	2	no	—
301	C₂×D₂₆₉	—	4	8	no	—
302	C₂×D₂₆₉	2₋¹⁺⁴	1	2	yes	—
303	C₄×C₂₆₉	—	2	1	no	—
304	C₄×C₂₆₉	—	2	2	no	—
305	C₄×C₂₆₉	—	2	1	no	—
306	C₄×C₂₆₉	—	2	2	no	—
307	C₄×C₂₆₉	—	2	2	no	—
308	C₄×C₂₆₉	—	2	1	no	—
309	C₄×C₂₆₉	—	2	1	no	—
310	C₄×C₂₆₉	—	2	1	no	—
311	C₄×C₂₆₉	C₂×#41	1	2	yes	—
312	Dic₂₆₉	—	2	1	no	—
313	Dic₂₆₉	—	2	1	no	—
314	Dic₂₆₉	—	2	2	no	—
315	Dic₂₆₉	—	2	2	no	—
316	Dic₂₆₉	—	2	2	no	—
317	Dic₂₆₉	—	2	1	no	—
318	Dic₂₆₉	—	2	1	no	—
319	Dic₂₆₉	—	2	1	no	—
320	Dic₂₆₉	H(5,𝔽₂)	1	2	yes	—
321	C₂×C₂₆₉	—	2	4	no	—
322	C₂×C₂₆₉	—	4	1	no	—
323	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
324	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₂₆₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
326	D₂₆₉	—	2	2	no	—
327	D₂₆₉	—	4	1	no	—
328	D₂₆₉	—	4	2	no	—
329	C₂₆₉	#3520	1	1	yes	characteristic, complemented, Sylow
330	#3520	—	269	1	no	maximal, Sylow
331	#556	—	269	1	no	—
332	#554	—	269	1	no	—
333	#554	—	269	1	no	—
334	#552	—	269	2	no	—
335	#551	—	269	2	no	—
336	#551	—	269	2	no	—
337	D₄×Q₈	—	269	1	no	—
338	#548	—	269	2	no	—
339	#547	—	269	1	no	—
340	#547	—	269	1	no	—
341	#546	—	269	1	no	—
342	#546	—	269	1	no	—
343	#542	—	269	1	no	—
344	#542	—	269	1	no	—
345	#539	—	269	2	no	—
346	#539	—	269	2	no	—
347	#533	—	269	1	no	—
348	#529	—	269	1	no	—
349	#525	—	269	2	no	—
350	C₂×C₂²⋊Q₈	—	269	2	no	—
351	#520	—	269	1	no	—
352	#520	D₂₆₉	1	1	yes	characteristic, complemented
353	C₂×C₄×D₄	—	269	1	no	—
354	C₂×#41	—	269	1	no	—
355	C₂×#41	—	269	2	no	—
356	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic
357	C₂²×Q₈	—	269	2	no	—
358	C₂²×D₄	—	269	1	no	—
359	C₂³×C₄	—	269	2	no	—
360	C₄⋊Q₈	—	269	1	no	—
361	C₄⋊Q₈	—	269	1	no	—
362	C₄⋊Q₈	—	269	1	no	—
363	C₄⋊Q₈	—	269	1	no	—
364	#126	—	269	1	no	—
365	#126	—	269	2	no	—
366	#126	—	269	2	no	—
367	#126	—	269	1	no	—
368	#126	—	269	2	no	—
369	#126	—	269	2	no	—
370	#125	—	269	1	no	—
371	#125	—	269	2	no	—
372	#125	—	269	2	no	—
373	#125	—	269	2	no	—
374	#124	—	269	1	no	—
375	#124	—	269	1	no	—
376	#124	—	269	2	no	—
377	#124	—	269	1	no	—
378	#124	—	269	2	no	—
379	#123	—	269	2	no	—
380	#123	—	269	2	no	—
381	#123	—	269	2	no	—
382	#123	—	269	2	no	—
383	#123	—	269	2	no	—
384	#123	—	269	1	no	—
385	#123	—	269	2	no	—
386	#123	—	269	2	no	—
387	#123	—	269	1	no	—
388	#123	—	269	2	no	—
389	C₂²⋊Q₈	—	269	1	no	—
390	C₂²⋊Q₈	—	269	1	no	—
391	C₂²⋊Q₈	—	269	2	no	—
392	C₂²⋊Q₈	—	269	2	no	—
393	C₂²⋊Q₈	—	269	1	no	—
394	C₂²⋊Q₈	—	269	1	no	—
395	C₂²⋊Q₈	—	269	2	no	—
396	C₂²⋊Q₈	—	269	2	no	—
397	C₂²⋊Q₈	—	269	2	no	—
398	C₂²⋊Q₈	—	269	2	no	—
399	C₂²⋊Q₈	—	269	2	no	—
400	C₂²⋊Q₈	—	269	2	no	—
401	C₂²⋊Q₈	—	269	2	no	—
402	C₂²⋊Q₈	—	269	1	no	—
403	C₂²⋊Q₈	—	269	2	no	—
404	C₂²⋊Q₈	—	269	2	no	—
405	C₂²⋊Q₈	—	269	2	no	—
406	#121	—	269	2	no	—
407	#121	—	269	2	no	—
408	#121	—	269	2	no	—
409	#121	—	269	1	no	—
410	#121	—	269	1	no	—
411	#121	—	269	1	no	—
412	#120	—	269	2	no	—
413	#120	—	269	2	no	—
414	C₄×Q₈	—	269	1	no	—
415	C₄×Q₈	—	269	1	no	—
416	C₄×Q₈	—	269	1	no	—
417	C₄×Q₈	—	269	2	no	—
418	C₄×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
419	C₄×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
420	C₄×D₄	—	269	1	no	—
421	C₄×D₄	—	269	1	no	—
422	C₄×D₄	—	269	2	no	—
423	C₄×D₄	—	269	2	no	—
424	C₄×D₄	—	269	2	no	—
425	C₄×D₄	—	269	1	no	—
426	C₄×D₄	—	269	1	no	—
427	C₄×D₄	—	269	1	no	—
428	C₄×D₄	—	269	2	no	—
429	C₄×D₄	—	269	2	no	—
430	C₄×D₄	—	269	1	no	—
431	C₄×D₄	—	269	2	no	—
432	C₄×D₄	—	269	1	no	—
433	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
434	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
435	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
436	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
437	#117	—	269	2	no	—
438	#117	—	269	1	no	—
439	#117	—	269	2	no	—
440	#117	—	269	2	no	—
441	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
442	#117	C₂×D₂₆₉	1	2	yes	complemented
443	C₂×C₄⋊C₄	—	269	2	no	—
444	C₂×C₄⋊C₄	—	269	2	no	—
445	C₂×C₄⋊C₄	—	269	1	no	—
446	C₂×C₄⋊C₄	—	269	1	no	—
447	C₂×C₄⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
448	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
449	C₂×C₂²⋊C₄	—	269	2	no	—
450	C₂×C₂²⋊C₄	—	269	2	no	—
451	C₂×C₂²⋊C₄	—	269	2	no	—
452	C₂×C₄²	—	269	1	no	—
453	C₂⁴	—	269	2	no	—
454	#41	—	2	4	no	—
455	#41	—	538	4	no	—
456	#41	—	1076	4	no	—
457	C₂×Q₈	—	269	1	no	—
458	C₂×Q₈	—	269	1	no	—
459	C₂×Q₈	—	269	2	no	—
460	C₂×Q₈	—	269	2	no	—
461	C₂×Q₈	—	269	2	no	—
462	C₂×Q₈	—	1076	4	no	—
463	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
464	C₂×D₄	—	269	1	no	—
465	C₂×D₄	—	269	2	no	—
466	C₂×D₄	—	269	2	no	—
467	C₂×D₄	—	269	1	no	—
468	C₂×D₄	—	269	2	no	—
469	C₂×D₄	—	269	1	no	—
470	C₂×D₄	—	269	1	no	—
471	C₂×D₄	—	269	2	no	—
472	C₂×D₄	—	538	4	no	—
473	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
474	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
475	C₂²×C₄	—	269	2	no	—
476	C₂²×C₄	—	269	2	no	—
477	C₂²×C₄	—	269	2	no	—
478	C₂²×C₄	—	269	1	no	—
479	C₂²×C₄	—	269	1	no	—
480	C₂²×C₄	—	269	1	no	—
481	C₂²×C₄	—	269	1	no	—
482	C₂²×C₄	—	269	2	no	—
483	C₂²×C₄	—	269	2	no	—
484	C₂²×C₄	—	269	2	no	—
485	C₂²×C₄	—	269	2	no	—
486	C₂²×C₄	—	1076	4	no	—
487	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
488	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
490	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
491	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
492	C₄⋊C₄	—	269	1	no	—
493	C₄⋊C₄	—	269	2	no	—
494	C₄⋊C₄	—	269	1	no	—
495	C₄⋊C₄	—	269	2	no	—
496	C₄⋊C₄	—	269	2	no	—
497	C₄⋊C₄	—	269	1	no	—
498	C₄⋊C₄	—	269	1	no	—
499	C₄⋊C₄	—	269	2	no	—
500	C₄⋊C₄	—	269	2	no	—
501	C₄⋊C₄	—	269	2	no	—
502	C₄⋊C₄	—	269	2	no	—
503	C₄⋊C₄	—	269	1	no	—
504	C₄⋊C₄	—	269	1	no	—
505	C₄⋊C₄	—	269	2	no	—
506	C₄⋊C₄	—	269	2	no	—
507	C₄⋊C₄	—	269	2	no	—
508	C₄⋊C₄	—	269	2	no	—
509	C₄⋊C₄	—	269	1	no	—
510	C₄⋊C₄	—	269	1	no	—
511	C₄⋊C₄	—	269	2	no	—
512	C₄⋊C₄	—	269	2	no	—
513	C₄⋊C₄	—	269	1	no	—
514	C₄⋊C₄	—	269	1	no	—
515	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
518	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
520	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
521	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
522	C₂²⋊C₄	—	269	2	no	—
523	C₂²⋊C₄	—	269	2	no	—
524	C₂²⋊C₄	—	269	1	no	—
525	C₂²⋊C₄	—	269	2	no	—
526	C₂²⋊C₄	—	269	1	no	—
527	C₂²⋊C₄	—	269	1	no	—
528	C₂²⋊C₄	—	269	1	no	—
529	C₂²⋊C₄	—	269	2	no	—
530	C₂²⋊C₄	—	269	2	no	—
531	C₂²⋊C₄	—	269	2	no	—
532	C₂²⋊C₄	—	269	2	no	—
533	C₂²⋊C₄	—	269	2	no	—
534	C₂²⋊C₄	—	269	2	no	—
535	C₂²⋊C₄	—	269	2	no	—
536	C₂²⋊C₄	—	269	2	no	—
537	C₂²⋊C₄	—	269	1	no	—
538	C₂²⋊C₄	—	269	1	no	—
539	C₂²⋊C₄	—	269	2	no	—
540	C₂²⋊C₄	—	269	2	no	—
541	C₂²⋊C₄	—	269	1	no	—
542	C₂²⋊C₄	—	269	2	no	—
543	C₂²⋊C₄	—	269	1	no	—
544	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
548	C₄²	—	269	1	no	—
549	C₄²	—	269	1	no	—
550	C₄²	—	269	1	no	—
551	C₄²	—	269	2	no	—
552	C₄²	—	269	2	no	—
553	C₄²	—	269	1	no	—
554	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
555	C₄²	C₂²×D₂₆₉	1	2	yes	—
556	C₄²	C₂²×D₂₆₉	1	2	yes	—
557	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
558	C₂³	—	269	1	no	—
559	C₂³	—	269	2	no	—
560	C₂³	—	269	1	no	—
561	C₂³	—	538	4	no	—
562	C₂³	—	538	4	no	—
563	C₂³	—	1076	2	no	—
564	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
565	C₂³	C₂³×D₂₆₉	1	2	yes	—
566	Q₈	—	2	2	no	—
567	Q₈	—	538	2	no	—
568	Q₈	—	538	4	no	—
569	Q₈	—	538	2	no	—
570	Q₈	—	1076	2	no	—
571	Q₈	—	1076	2	no	—
572	D₄	—	2	4	no	—
573	D₄	—	538	2	no	—
574	D₄	—	538	2	no	—
575	D₄	—	538	2	no	—
576	D₄	—	538	4	no	—
577	D₄	—	538	4	no	—
578	D₄	—	538	2	no	—
579	D₄	—	1076	2	no	—
580	D₄	—	1076	2	no	—
581	D₄	#16864402	1	4	yes	complemented
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	269	1	no	—
588	C₂×C₄	—	269	1	no	—
589	C₂×C₄	—	269	1	no	—
590	C₂×C₄	—	269	2	no	—
591	C₂×C₄	—	269	1	no	—
592	C₂×C₄	—	269	1	no	—
593	C₂×C₄	—	269	2	no	—
594	C₂×C₄	—	269	1	no	—
595	C₂×C₄	—	269	2	no	—
596	C₂×C₄	—	538	2	no	—
597	C₂×C₄	—	538	4	no	—
598	C₂×C₄	—	538	2	no	—
599	C₂×C₄	—	538	4	no	—
600	C₂×C₄	—	538	4	no	—
601	C₂×C₄	—	538	2	no	—
602	C₂×C₄	—	538	2	no	—
603	C₂×C₄	—	1076	2	no	—
604	C₂×C₄	—	1076	2	no	—
605	C₂×C₄	—	1076	2	no	—
606	C₂×C₄	—	1076	2	no	—
607	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
610	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
612	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
614	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	269	2	no	—
622	C₂²	—	538	1	no	—
623	C₂²	—	538	1	no	—
624	C₂²	—	538	1	no	—
625	C₂²	—	538	2	no	—
626	C₂²	—	538	2	no	—
627	C₂²	—	538	1	no	—
628	C₂²	—	538	1	no	—
629	C₂²	—	538	2	no	—
630	C₂²	—	1076	8	no	—
631	C₂²	C₂×#16864402	1	4	yes	—
632	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	269	2	no	—
642	C₄	—	538	1	no	—
643	C₄	—	538	1	no	—
644	C₄	—	538	2	no	—
645	C₄	—	538	2	no	—
646	C₄	—	538	2	no	—
647	C₄	—	538	1	no	—
648	C₄	—	538	1	no	—
649	C₄	—	538	1	no	—
650	C₄	C₂×#16864402	1	2	yes	—
651	C₂	—	2	4	no	—
652	C₂	—	4	1	no	—
653	C₂	—	538	2	no	—
654	C₂	—	1076	2	no	—
655	C₂	—	1076	1	no	—
656	C₂	C₂²×#16864402	1	1	yes	characteristic
657	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
658	C₂	2₋¹⁺⁴×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#520×C₂₆₉	C₂
hypercenter	#520	D₂₆₉
hypocenter	C₂₆₉	#3520
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. #31771327	C₂	semidirect
2. #31771315	C₂	semidirect
3. #31771310	C₂	semidirect
4. #31771288	C₂	semidirect
5. #31771284	C₂	semidirect
6. #31771279	C₂	semidirect
7. D₄×Dic₅₃₈	C₂	semidirect
8. #31771264	C₂	semidirect
9. #31771256	C₂	semidirect
10. #31771254	C₂	semidirect
11. #31771250	C₂	semidirect
12. #31771243	C₂	semidirect
13. #31771227	C₂	semidirect
14. #31771226	C₂	semidirect
15. #31771202	C₂	semidirect
16. #31771197	C₂	semidirect
17. #31771159	C₂	semidirect
18. #31771133	C₂	semidirect
19. #31771114	C₂	semidirect
20. C₂×#22575431	C₂	semidirect
21. #31771084	C₂	semidirect
22. C₄×D₄×D₂₆₉	C₂	semidirect
23. #520×C₂₆₉	C₂	semidirect
24. C₂×#16864402	C₂²	semidirect
26. C₂²×Dic₅₃₈	C₂²	semidirect
29. #22575453	C₂²	semidirect
30. #22575452	C₂²	semidirect
31. #22575452	C₂²	semidirect
32. #22575451	C₂²	semidirect
33. #22575448	C₂²	semidirect
34. #22575448	C₂²	semidirect
35. #22575448	C₂²	semidirect
36. #22575447	C₂²	semidirect
37. #22575447	C₂²	semidirect
38. #22575446	C₂²	semidirect
39. #22575445	C₂²	semidirect
40. #22575443	C₂²	semidirect
41. #22575443	C₂²	semidirect
42. #22575443	C₂²	semidirect
45. #22575441	C₂²	semidirect
46. #22575439	C₂²	semidirect
47. #22575439	C₂²	semidirect
49. #22575438	C₂²	semidirect
50. #22575438	C₂²	semidirect
53. #22575436	C₂²	semidirect
54. #22575436	C₂²	semidirect
56. #22575435	C₂²	semidirect
57. #22575434	C₂²	semidirect
59. #22575432	C₂²	semidirect
60. #22575432	C₂²	semidirect
61. #22575432	C₂²	semidirect
66. #22575431	C₂²	semidirect
67. #22575431	C₂²	semidirect
68. #22575431	C₂²	semidirect
69. #22575431	C₂²	semidirect
70. #22575431	C₂²	semidirect
71. #22575430	C₂²	semidirect
72. #22575430	C₂²	semidirect
74. #22575429	C₂²	semidirect
80. #22575425	C₂²	semidirect
83. C₄×Dic₅₃₈	C₂²	semidirect
84. C₄×Dic₅₃₈	C₂²	semidirect
85. C₄×Dic₅₃₈	C₂²	semidirect
86. #22575418	C₂²	semidirect
96. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
97. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
99. #22575413	C₂²	semidirect
101. #22575410	C₂²	semidirect
102. #22575410	C₂²	semidirect
103. #22575409	C₂²	semidirect
104. C₂×#16864381	C₂²	semidirect
105. C₂×#16864381	C₂²	semidirect
107. C₄⋊C₄×D₂₆₉	C₂²	semidirect
113. C₄×Q₈×C₂₆₉	C₂²	semidirect
114. C₄×Q₈×C₂₆₉	C₂²	semidirect
117. C₄×D₄×C₂₆₉	C₂²	semidirect
118. C₄×D₄×C₂₆₉	C₂²	semidirect
119. #117×C₂₆₉	C₂²	semidirect
120. #117×C₂₆₉	C₂²	semidirect
121. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
271. D₄×C₂₆₉	#41	semidirect
329. C₂₆₉	#3520	semidirect
352. #520	D₂₆₉	semidirect
418. C₄×Q₈	C₂×D₂₆₉	semidirect
419. C₄×Q₈	C₂×D₂₆₉	semidirect
435. C₄×D₄	C₂×D₂₆₉	semidirect
436. C₄×D₄	C₂×D₂₆₉	semidirect
441. #117	C₂×D₂₆₉	semidirect
442. #117	C₂×D₂₆₉	semidirect
447. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
448. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
581. D₄	#16864402	semidirect

Maximal subgroups

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

subgroup	index
#31771327	2
#31771315	2
#31771310	2
#31771288	2
#31771284	2
#31771279	2
D₄×Dic₅₃₈	2
#31771264	2
#31771256	2
#31771254	2
#31771250	2
#31771243	2
#31771227	2
#31771226	2
#31771202	2
#31771197	2
#31771159	2
#31771133	2
#31771114	2
C₂×#22575431	2
#31771084	2
C₄×D₄×D₂₆₉	2
#520×C₂₆₉	2
#3520	269