Subgroups — #46824960

Order 34432.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 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	#31771323	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771311	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771303	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771299	C₂	1	2	yes	maximal, complemented
6	#31771293	C₂	1	2	yes	maximal, complemented
7	#31771283	C₂	1	2	yes	maximal, complemented
8	#31771280	C₂	1	2	yes	maximal, complemented
9	#31771257	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771251	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771246	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771228	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771215	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771203	C₂	1	2	yes	maximal, complemented
15	#31771191	C₂	1	2	yes	maximal, complemented
16	#31771140	C₂	1	1	yes	maximal, characteristic, complemented
17	#31771137	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771133	C₂	1	2	yes	maximal, complemented
19	#126×D₂₆₉	C₂	1	2	yes	maximal, complemented
20	#31771086	C₂	1	1	yes	maximal, characteristic, complemented
21	#31771079	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#16864403	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16864403	C₂²	1	1	yes	characteristic
25	C₂×#16864402	C₂²	1	1	yes	characteristic
26	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic
27	#22575452	C₂²	1	1	yes	characteristic, complemented
28	#22575451	C₂²	1	1	yes	characteristic, complemented
29	#22575448	C₂²	1	2	yes	complemented
30	#22575448	C₂²	1	2	yes	complemented
31	#22575448	C₂²	1	2	yes	complemented
32	#22575448	C₂²	1	2	yes	complemented
33	#22575447	C₂²	1	2	yes	complemented
34	#22575447	C₂²	1	2	yes	complemented
35	#22575446	C₂²	1	1	yes	characteristic
36	#22575446	C₂²	1	2	yes	—
37	#22575446	C₂²	1	2	yes	—
38	#22575446	C₂²	1	2	yes	—
39	#22575446	C₂²	1	1	yes	characteristic, complemented
40	#22575444	C₂²	1	1	yes	characteristic, complemented
41	#22575444	C₂²	1	2	yes	complemented
42	#22575444	C₂²	1	1	yes	characteristic, complemented
43	#22575443	C₂²	1	2	yes	complemented
44	#22575442	C₂²	1	1	yes	characteristic
45	#22575441	C₂²	1	1	yes	characteristic
46	#22575440	C₂²	1	1	yes	characteristic
47	#22575439	C₂²	1	2	yes	—
48	#22575439	C₂²	1	2	yes	complemented
49	#22575438	C₂²	1	2	yes	—
50	#22575438	C₂²	1	2	yes	—
51	#22575438	C₂²	1	2	yes	complemented
52	#22575438	C₂²	1	2	yes	complemented
53	#22575438	C₂²	1	2	yes	complemented
54	#22575435	C₂²	1	1	yes	characteristic
55	#22575435	C₂²	1	1	yes	characteristic, complemented
56	#22575435	C₂²	1	2	yes	complemented
57	#22575435	C₂²	1	2	yes	complemented
58	#22575433	C₂²	1	1	yes	characteristic, complemented
59	#22575433	C₂²	1	1	yes	characteristic, complemented
60	#22575433	C₂²	1	2	yes	complemented
61	#22575433	C₂²	1	2	yes	complemented
62	#22575432	C₂²	1	1	yes	characteristic
63	#22575431	C₂²	1	2	yes	complemented
64	#22575431	C₂²	1	2	yes	complemented
65	#22575431	C₂²	1	2	yes	complemented
66	#22575428	C₂²	1	1	yes	characteristic
67	#22575428	C₂²	1	2	yes	—
68	#22575427	C₂²	1	1	yes	characteristic
69	#22575427	C₂²	1	2	yes	complemented
70	#22575426	C₂²	1	2	yes	—
71	#22575426	C₂²	1	2	yes	complemented
72	#22575424	C₂²	1	1	yes	characteristic
73	#22575423	C₂²	1	2	yes	—
74	#22575421	C₂²	1	2	yes	—
75	Q₈×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
78	#22575418	C₂²	1	1	yes	characteristic, complemented
79	#22575418	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₁₀₇₆	C₂²	1	2	yes	—
81	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
82	C₄×D₁₀₇₆	C₂²	1	2	yes	—
83	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
84	#22575415	C₂²	1	1	yes	characteristic
85	#22575415	C₂²	1	1	yes	characteristic
86	#22575415	C₂²	1	1	yes	characteristic
87	#22575415	C₂²	1	1	yes	characteristic
88	#22575415	C₂²	1	1	yes	characteristic
89	#22575415	C₂²	1	2	yes	complemented
90	#22575415	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
96	#22575412	C₂²	1	1	yes	characteristic
97	#22575412	C₂²	1	1	yes	characteristic, complemented
98	#22575411	C₂²	1	2	yes	complemented
99	#22575411	C₂²	1	2	yes	complemented
100	#22575411	C₂²	1	2	yes	complemented
101	#22575411	C₂²	1	1	yes	characteristic, complemented
102	#22575410	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
110	C₄²×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₂₆₉	C₂²	1	2	yes	complemented
112	#126×C₂₆₉	C₂²	1	2	yes	—
113	#125×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
114	#125×C₂₆₉	C₂²	1	2	yes	complemented
115	#123×C₂₆₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
120	#117×C₂₆₉	C₂²	1	1	yes	characteristic
121	#117×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	#16864403	—	2	4	no	—
125	#16864402	—	2	4	no	—
126	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₅₃₈	C₂³	1	2	yes	—
129	C₂×D₁₀₇₆	—	2	4	no	—
130	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
131	C₂×D₁₀₇₆	C₂³	1	2	yes	—
132	C₂×D₁₀₇₆	C₂³	1	2	yes	—
133	C₂×D₁₀₇₆	C₂³	1	2	yes	—
134	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
140	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
142	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
143	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
144	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
147	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
148	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
149	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
150	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
152	C₄⋊Dic₂₆₉	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	1	yes	characteristic
158	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
159	#16864381	C₂³	1	1	yes	characteristic
160	#16864381	C₂³	1	1	yes	characteristic
161	#16864381	C₂³	1	2	yes	—
162	#16864381	C₂³	1	2	yes	—
163	#16864381	C₂³	1	2	yes	—
164	#16864381	C₂³	1	2	yes	—
165	#16864381	C₂³	1	1	yes	characteristic
166	#16864381	C₂³	1	2	yes	—
167	#16864381	C₂³	1	1	yes	characteristic
168	#16864381	C₂³	1	2	yes	—
169	#16864381	C₂³	1	2	yes	—
170	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
177	#16864379	C₂³	1	2	yes	—
178	#16864379	C₂³	1	2	yes	—
179	#16864379	C₂³	1	2	yes	—
180	#16864379	C₂³	1	2	yes	—
181	#16864379	C₂³	1	2	yes	—
182	#16864379	C₂³	1	2	yes	—
183	#16864379	C₂³	1	2	yes	—
184	#16864379	C₂³	1	2	yes	—
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	1	yes	characteristic
191	#16864379	C₂³	1	1	yes	characteristic
192	#16864379	C₂³	1	2	yes	—
193	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₂₆₉	C₂³	1	2	yes	—
196	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₂₆₉	C₂³	1	2	yes	—
198	C₄×Dic₂₆₉	C₂³	1	2	yes	—
199	C₄×Dic₂₆₉	C₂³	1	2	yes	—
200	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
207	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
208	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
210	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
212	C₄⋊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	2	yes	—
216	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
222	C₄²×C₂₆₉	C₂³	1	2	yes	—
223	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
224	C₄²×C₂₆₉	C₂³	1	2	yes	—
225	C₂²×D₂₆₉	—	2	4	no	—
226	C₂²×D₂₆₉	—	4	2	no	—
227	C₂²×D₂₆₉	—	4	2	no	—
228	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
229	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
231	Dic₅₃₈	—	2	2	no	—
232	Dic₅₃₈	—	4	1	no	—
233	Dic₅₃₈	—	4	2	no	—
234	D₁₀₇₆	—	2	4	no	—
235	D₁₀₇₆	—	2	4	no	—
236	D₁₀₇₆	—	2	2	no	—
237	D₁₀₇₆	—	4	2	no	—
238	D₁₀₇₆	#41	1	4	yes	—
239	C₂²⋊D₂₆₉	—	2	4	no	—
240	C₂²⋊D₂₆₉	—	4	1	no	—
241	C₂²⋊D₂₆₉	—	4	2	no	—
242	C₂²⋊D₂₆₉	—	4	1	no	—
243	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
248	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
249	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
252	C₄×D₂₆₉	—	2	4	no	—
253	C₄×D₂₆₉	—	2	4	no	—
254	C₄×D₂₆₉	—	2	2	no	—
255	C₄×D₂₆₉	—	4	2	no	—
256	C₄×D₂₆₉	—	4	1	no	—
257	C₄×D₂₆₉	—	4	1	no	—
258	C₄×D₂₆₉	—	4	2	no	—
259	C₄×D₂₆₉	—	4	2	no	—
260	C₄×D₂₆₉	—	4	2	no	—
261	C₄×D₂₆₉	—	4	2	no	—
262	C₄×D₂₆₉	—	4	2	no	—
263	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
264	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
265	Q₈×C₂₆₉	—	2	2	no	—
266	D₄×C₂₆₉	—	4	1	no	—
267	C₂×C₄×C₂₆₉	—	2	2	no	—
268	C₂×C₄×C₂₆₉	—	2	2	no	—
269	C₂×C₄×C₂₆₉	—	4	2	no	—
270	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
272	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
274	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
275	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
277	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₂₆₉	—	2	1	no	—
280	C₂²×C₂₆₉	—	2	1	no	—
281	C₂²×C₂₆₉	—	2	1	no	—
282	C₂²×C₂₆₉	—	2	1	no	—
283	C₂²×C₂₆₉	—	2	1	no	—
284	C₂²×C₂₆₉	—	2	1	no	—
285	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
286	C₂×D₂₆₉	—	2	2	no	—
287	C₂×D₂₆₉	—	2	2	no	—
288	C₂×D₂₆₉	—	2	1	no	—
289	C₂×D₂₆₉	—	2	2	no	—
290	C₂×D₂₆₉	—	2	1	no	—
291	C₂×D₂₆₉	—	2	2	no	—
292	C₂×D₂₆₉	—	2	1	no	—
293	C₂×D₂₆₉	—	2	2	no	—
294	C₂×D₂₆₉	—	8	4	no	—
295	C₂×D₂₆₉	C₂×#41	1	4	yes	—
296	C₄×C₂₆₉	—	2	1	no	—
297	C₄×C₂₆₉	—	2	1	no	—
298	C₄×C₂₆₉	—	2	2	no	—
299	C₄×C₂₆₉	—	2	2	no	—
300	C₄×C₂₆₉	—	2	2	no	—
301	C₄×C₂₆₉	—	2	1	no	—
302	C₄×C₂₆₉	—	2	1	no	—
303	C₄×C₂₆₉	—	2	2	no	—
304	C₄×C₂₆₉	C₂×#41	1	2	yes	—
305	Dic₂₆₉	—	2	1	no	—
306	Dic₂₆₉	—	2	2	no	—
307	Dic₂₆₉	—	2	1	no	—
308	Dic₂₆₉	—	2	1	no	—
309	Dic₂₆₉	—	2	1	no	—
310	Dic₂₆₉	—	2	1	no	—
311	Dic₂₆₉	—	2	1	no	—
312	Dic₂₆₉	—	2	2	no	—
313	Dic₂₆₉	—	2	1	no	—
314	C₂×C₂₆₉	—	4	1	no	—
315	C₂×C₂₆₉	—	4	1	no	—
316	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
317	C₂×C₂₆₉	#585	1	1	yes	characteristic
318	C₂×C₂₆₉	#585	1	1	yes	characteristic
319	D₂₆₉	—	2	4	no	—
320	D₂₆₉	—	4	1	no	—
321	D₂₆₉	—	4	2	no	—
322	C₂₆₉	#3521	1	1	yes	characteristic, complemented, Sylow
323	#3521	—	269	1	no	maximal, Sylow
324	#556	—	269	1	no	—
325	#556	—	269	1	no	—
326	#554	—	269	1	no	—
327	#553	—	269	2	no	—
328	#553	—	269	1	no	—
329	#552	—	269	2	no	—
330	#552	D₂₆₉	1	1	yes	characteristic, complemented
331	#551	—	269	2	no	—
332	#551	—	269	2	no	—
333	#547	—	269	1	no	—
334	#546	—	269	1	no	—
335	#546	—	269	1	no	—
336	#542	—	269	1	no	—
337	#541	—	269	1	no	—
338	#539	—	269	2	no	—
339	#538	—	269	2	no	—
340	#529	—	269	1	no	—
341	#529	—	269	1	no	—
342	#529	—	269	2	no	—
343	C₂×#126	—	269	2	no	—
344	#520	—	269	1	no	—
345	#518	—	269	1	no	—
346	C₄×#41	—	269	1	no	—
347	C₂×#41	—	269	1	no	—
348	C₂×#41	—	269	1	no	—
349	C₂²×D₄	—	269	1	no	—
350	C₄⋊Q₈	—	269	1	no	—
351	C₄⋊Q₈	—	269	1	no	—
352	#126	—	269	2	no	—
353	#126	—	269	2	no	—
354	#126	—	269	2	no	—
355	#126	—	269	2	no	—
356	#126	—	269	1	no	—
357	#126	—	269	2	no	—
358	#126	—	269	2	no	—
359	#126	—	269	1	no	—
360	#126	—	269	2	no	—
361	#126	—	269	2	no	—
362	#126	—	269	2	no	—
363	#126	C₂×D₂₆₉	1	2	yes	—
364	#125	—	269	2	no	—
365	#125	—	269	1	no	—
366	#125	—	269	2	no	—
367	#125	—	269	1	no	—
368	#125	C₂×D₂₆₉	1	1	yes	characteristic, complemented
369	#125	C₂×D₂₆₉	1	2	yes	complemented
370	#124	—	269	1	no	—
371	#124	—	269	1	no	—
372	#124	—	269	2	no	—
373	#124	—	269	2	no	—
374	#124	—	269	1	no	—
375	#123	—	269	2	no	—
376	#123	—	269	2	no	—
377	#123	—	269	2	no	—
378	#123	—	269	2	no	—
379	#123	—	269	2	no	—
380	#123	—	269	2	no	—
381	#123	—	269	1	no	—
382	#123	—	269	1	no	—
383	#123	—	269	2	no	—
384	#123	C₂×D₂₆₉	1	2	yes	—
385	C₂²⋊Q₈	—	269	1	no	—
386	C₂²⋊Q₈	—	269	1	no	—
387	C₂²⋊Q₈	—	269	1	no	—
388	C₂²⋊Q₈	—	269	2	no	—
389	C₂²⋊Q₈	—	269	2	no	—
390	C₂²⋊Q₈	—	269	2	no	—
391	C₂²⋊Q₈	—	269	2	no	—
392	C₂²⋊Q₈	—	269	2	no	—
393	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic
394	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
395	#121	—	269	1	no	—
396	#121	—	269	2	no	—
397	#121	—	269	1	no	—
398	#121	—	269	1	no	—
399	#121	—	269	2	no	—
400	#121	—	269	2	no	—
401	#121	—	269	2	no	—
402	#120	—	269	2	no	—
403	#120	—	269	2	no	—
404	C₄×Q₈	—	269	1	no	—
405	C₄×Q₈	—	269	1	no	—
406	C₄×Q₈	—	269	1	no	—
407	C₄×Q₈	—	269	2	no	—
408	C₄×Q₈	—	269	1	no	—
409	C₄×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
410	C₄×D₄	—	269	2	no	—
411	C₄×D₄	—	269	2	no	—
412	C₄×D₄	—	269	1	no	—
413	C₄×D₄	—	269	1	no	—
414	C₄×D₄	—	269	2	no	—
415	C₄×D₄	—	269	1	no	—
416	C₄×D₄	—	269	2	no	—
417	C₄×D₄	—	269	1	no	—
418	C₄×D₄	—	269	1	no	—
419	C₄×D₄	—	269	1	no	—
420	C₄×D₄	—	269	1	no	—
421	C₄×D₄	—	269	2	no	—
422	C₄×D₄	—	269	1	no	—
423	C₄×D₄	—	269	2	no	—
424	C₄×D₄	—	269	2	no	—
425	C₄×D₄	—	269	2	no	—
426	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
427	#117	—	269	1	no	—
428	#117	—	269	1	no	—
429	#117	—	269	2	no	—
430	#117	—	269	1	no	—
431	#117	—	269	2	no	—
432	#117	—	269	2	no	—
433	#117	—	269	2	no	—
434	#117	C₂×D₂₆₉	1	1	yes	characteristic
435	#117	C₂×D₂₆₉	1	2	yes	complemented
436	C₂×C₄⋊C₄	—	269	2	no	—
437	C₂×C₄⋊C₄	—	269	2	no	—
438	C₂×C₄⋊C₄	—	269	2	no	—
439	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
440	C₂×C₂²⋊C₄	—	269	2	no	—
441	C₂×C₂²⋊C₄	—	269	2	no	—
442	C₂×C₂²⋊C₄	—	269	2	no	—
443	C₂×C₂²⋊C₄	—	269	2	no	—
444	C₂×C₄²	—	269	2	no	—
445	C₂×C₄²	—	269	1	no	—
446	C₂⁴	—	269	2	no	—
447	#41	—	538	4	no	—
448	#41	—	538	4	no	—
449	C₂×Q₈	—	269	1	no	—
450	C₂×Q₈	—	269	1	no	—
451	C₂×Q₈	—	269	2	no	—
452	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
453	C₂×D₄	—	269	2	no	—
454	C₂×D₄	—	269	1	no	—
455	C₂×D₄	—	269	2	no	—
456	C₂×D₄	—	269	1	no	—
457	C₂×D₄	—	269	1	no	—
458	C₂×D₄	—	269	2	no	—
459	C₂×D₄	—	269	2	no	—
460	C₂×D₄	—	269	1	no	—
461	C₂×D₄	—	269	2	no	—
462	C₂×D₄	—	538	4	no	—
463	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
464	C₂²×C₄	—	269	2	no	—
465	C₂²×C₄	—	269	1	no	—
466	C₂²×C₄	—	269	2	no	—
467	C₂²×C₄	—	269	2	no	—
468	C₂²×C₄	—	269	2	no	—
469	C₂²×C₄	—	269	1	no	—
470	C₂²×C₄	—	269	1	no	—
471	C₂²×C₄	—	269	2	no	—
472	C₂²×C₄	—	269	2	no	—
473	C₂²×C₄	—	269	2	no	—
474	C₂²×C₄	—	269	2	no	—
475	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
478	C₄⋊C₄	—	269	1	no	—
479	C₄⋊C₄	—	269	1	no	—
480	C₄⋊C₄	—	269	1	no	—
481	C₄⋊C₄	—	269	2	no	—
482	C₄⋊C₄	—	269	2	no	—
483	C₄⋊C₄	—	269	2	no	—
484	C₄⋊C₄	—	269	2	no	—
485	C₄⋊C₄	—	269	2	no	—
486	C₄⋊C₄	—	269	2	no	—
487	C₄⋊C₄	—	269	1	no	—
488	C₄⋊C₄	—	269	1	no	—
489	C₄⋊C₄	—	269	1	no	—
490	C₄⋊C₄	—	269	1	no	—
491	C₄⋊C₄	—	269	1	no	—
492	C₄⋊C₄	—	269	2	no	—
493	C₄⋊C₄	—	269	2	no	—
494	C₄⋊C₄	—	269	1	no	—
495	C₄⋊C₄	—	269	2	no	—
496	C₄⋊C₄	—	269	1	no	—
497	C₄⋊C₄	—	269	2	no	—
498	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
499	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
500	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
501	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
504	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
505	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
507	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
508	C₂²⋊C₄	—	269	1	no	—
509	C₂²⋊C₄	—	269	1	no	—
510	C₂²⋊C₄	—	269	1	no	—
511	C₂²⋊C₄	—	269	2	no	—
512	C₂²⋊C₄	—	269	1	no	—
513	C₂²⋊C₄	—	269	1	no	—
514	C₂²⋊C₄	—	269	1	no	—
515	C₂²⋊C₄	—	269	2	no	—
516	C₂²⋊C₄	—	269	2	no	—
517	C₂²⋊C₄	—	269	2	no	—
518	C₂²⋊C₄	—	269	2	no	—
519	C₂²⋊C₄	—	269	2	no	—
520	C₂²⋊C₄	—	269	2	no	—
521	C₂²⋊C₄	—	269	2	no	—
522	C₂²⋊C₄	—	269	2	no	—
523	C₂²⋊C₄	—	269	2	no	—
524	C₂²⋊C₄	—	269	2	no	—
525	C₂²⋊C₄	—	269	2	no	—
526	C₂²⋊C₄	—	269	2	no	—
527	C₂²⋊C₄	—	269	2	no	—
528	C₂²⋊C₄	—	269	1	no	—
529	C₂²⋊C₄	—	269	2	no	—
530	C₂²⋊C₄	—	269	1	no	—
531	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
533	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
536	C₄²	—	269	1	no	—
537	C₄²	—	269	1	no	—
538	C₄²	—	269	1	no	—
539	C₄²	—	269	2	no	—
540	C₄²	—	269	2	no	—
541	C₄²	—	269	2	no	—
542	C₄²	—	269	2	no	—
543	C₄²	—	269	1	no	—
544	C₄²	—	269	1	no	—
545	C₄²	C₂²×D₂₆₉	1	2	yes	—
546	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
547	C₄²	C₂²×D₂₆₉	1	2	yes	—
548	C₂³	—	269	2	no	—
549	C₂³	—	269	2	no	—
550	C₂³	—	269	1	no	—
551	C₂³	—	538	4	no	—
552	C₂³	—	1076	2	no	—
553	C₂³	—	1076	2	no	—
554	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
555	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	538	2	no	—
558	Q₈	—	1076	1	no	—
559	Q₈	—	1076	2	no	—
560	D₄	—	4	1	no	—
561	D₄	—	269	4	no	—
562	D₄	—	538	4	no	—
563	D₄	—	538	4	no	—
564	D₄	—	538	4	no	—
565	D₄	—	538	2	no	—
566	D₄	—	1076	2	no	—
567	D₄	—	1076	1	no	—
568	D₄	—	1076	2	no	—
569	D₄	—	1076	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	269	1	no	—
574	C₂×C₄	—	269	1	no	—
575	C₂×C₄	—	269	1	no	—
576	C₂×C₄	—	269	1	no	—
577	C₂×C₄	—	269	2	no	—
578	C₂×C₄	—	269	2	no	—
579	C₂×C₄	—	269	1	no	—
580	C₂×C₄	—	269	1	no	—
581	C₂×C₄	—	269	1	no	—
582	C₂×C₄	—	538	4	no	—
583	C₂×C₄	—	538	4	no	—
584	C₂×C₄	—	538	2	no	—
585	C₂×C₄	—	1076	2	no	—
586	C₂×C₄	—	1076	2	no	—
587	C₂×C₄	—	1076	2	no	—
588	C₂×C₄	—	1076	1	no	—
589	C₂×C₄	—	1076	1	no	—
590	C₂×C₄	—	1076	2	no	—
591	C₂×C₄	—	1076	2	no	—
592	C₂×C₄	—	1076	2	no	—
593	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
594	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
597	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
598	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
600	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	269	4	no	—
609	C₂²	—	538	2	no	—
610	C₂²	—	538	2	no	—
611	C₂²	—	538	1	no	—
612	C₂²	—	538	2	no	—
613	C₂²	—	538	1	no	—
614	C₂²	—	538	2	no	—
615	C₂²	—	538	1	no	—
616	C₂²	—	538	2	no	—
617	C₂²	—	2152	4	no	—
618	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	2	no	—
627	C₄	—	538	1	no	—
628	C₄	—	538	2	no	—
629	C₄	—	538	1	no	—
630	C₄	—	538	1	no	—
631	C₄	—	538	1	no	—
632	C₄	—	538	1	no	—
633	C₄	—	538	1	no	—
634	C₄	—	538	2	no	—
635	C₄	—	538	1	no	—
636	C₄	#41×D₂₆₉	1	2	yes	—
637	C₂	—	4	1	no	—
638	C₂	—	4	1	no	—
639	C₂	—	538	4	no	—
640	C₂	—	1076	2	no	—
641	C₂	—	1076	1	no	—
642	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
643	C₂	#31771441	1	1	yes	characteristic
644	C₂	#31771442	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#552×C₂₆₉	C₂
hypercenter	#552	D₂₆₉
hypocenter	C₂₆₉	#3521
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #31771327	C₂	semidirect
2. #31771323	C₂	semidirect
3. #31771311	C₂	semidirect
4. #31771303	C₂	semidirect
5. #31771299	C₂	semidirect
6. #31771293	C₂	semidirect
7. #31771283	C₂	semidirect
8. #31771280	C₂	semidirect
9. #31771257	C₂	semidirect
10. #31771251	C₂	semidirect
11. #31771246	C₂	semidirect
12. #31771228	C₂	semidirect
13. #31771215	C₂	semidirect
14. #31771203	C₂	semidirect
15. #31771191	C₂	semidirect
16. #31771140	C₂	semidirect
17. #31771137	C₂	semidirect
18. #31771133	C₂	semidirect
19. #126×D₂₆₉	C₂	semidirect
20. #31771086	C₂	semidirect
21. #31771079	C₂	semidirect
22. C₄×#16864403	C₂	semidirect
23. #552×C₂₆₉	C₂	semidirect
27. #22575452	C₂²	semidirect
28. #22575451	C₂²	semidirect
29. #22575448	C₂²	semidirect
30. #22575448	C₂²	semidirect
31. #22575448	C₂²	semidirect
32. #22575448	C₂²	semidirect
33. #22575447	C₂²	semidirect
34. #22575447	C₂²	semidirect
39. #22575446	C₂²	semidirect
40. #22575444	C₂²	semidirect
41. #22575444	C₂²	semidirect
42. #22575444	C₂²	semidirect
43. #22575443	C₂²	semidirect
48. #22575439	C₂²	semidirect
51. #22575438	C₂²	semidirect
52. #22575438	C₂²	semidirect
53. #22575438	C₂²	semidirect
55. #22575435	C₂²	semidirect
56. #22575435	C₂²	semidirect
57. #22575435	C₂²	semidirect
58. #22575433	C₂²	semidirect
59. #22575433	C₂²	semidirect
60. #22575433	C₂²	semidirect
61. #22575433	C₂²	semidirect
63. #22575431	C₂²	semidirect
64. #22575431	C₂²	semidirect
65. #22575431	C₂²	semidirect
69. #22575427	C₂²	semidirect
71. #22575426	C₂²	semidirect
75. Q₈×Dic₂₆₉	C₂²	semidirect
76. C₄×Dic₅₃₈	C₂²	semidirect
77. C₄×Dic₅₃₈	C₂²	semidirect
78. #22575418	C₂²	semidirect
79. #22575418	C₂²	semidirect
83. C₄×D₁₀₇₆	C₂²	semidirect
89. #22575415	C₂²	semidirect
90. #22575415	C₂²	semidirect
92. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
93. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
94. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
95. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
97. #22575412	C₂²	semidirect
98. #22575411	C₂²	semidirect
99. #22575411	C₂²	semidirect
100. #22575411	C₂²	semidirect
101. #22575411	C₂²	semidirect
102. #22575410	C₂²	semidirect
103. C₄⋊C₄×D₂₆₉	C₂²	semidirect
104. C₄⋊C₄×D₂₆₉	C₂²	semidirect
105. C₄⋊C₄×D₂₆₉	C₂²	semidirect
110. C₄²×D₂₆₉	C₂²	semidirect
111. C₄²×D₂₆₉	C₂²	semidirect
113. #125×C₂₆₉	C₂²	semidirect
114. #125×C₂₆₉	C₂²	semidirect
117. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
118. C₄×Q₈×C₂₆₉	C₂²	semidirect
121. #117×C₂₆₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
322. C₂₆₉	#3521	semidirect
330. #552	D₂₆₉	semidirect
368. #125	C₂×D₂₆₉	semidirect
369. #125	C₂×D₂₆₉	semidirect
394. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
409. C₄×Q₈	C₂×D₂₆₉	semidirect
435. #117	C₂×D₂₆₉	semidirect
439. C₂×C₄⋊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
#31771327	2
#31771323	2
#31771311	2
#31771303	2
#31771299	2
#31771293	2
#31771283	2
#31771280	2
#31771257	2
#31771251	2
#31771246	2
#31771228	2
#31771215	2
#31771203	2
#31771191	2
#31771140	2
#31771137	2
#31771133	2
#126×D₂₆₉	2
#31771086	2
#31771079	2
C₄×#16864403	2
#552×C₂₆₉	2
#3521	269