Subgroups — C₂×#137×D₂₆₉ #46825621

Order 34432.

1464 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₆₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Q₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22575486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#22575485	C₂	1	2	yes	maximal, complemented
5	C₂×#22575484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22575483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22575482	C₂	1	2	yes	maximal, complemented
8	#137×D₂₆₉	C₂	1	16	yes	maximal, direct product factor
9	C₂×Q₁₆×D₂₆₉	C₂	1	2	yes	maximal, complemented
10	C₂×SD₁₆×D₂₆₉	C₂	1	2	yes	maximal, complemented
11	C₂×M₁₆×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16864403	C₂²	1	1	yes	characteristic
14	C₂×#16864402	—	2	1	no	—
15	C₂×#16864402	C₂²	1	1	yes	characteristic
16	C₂×#16864401	—	2	1	no	—
17	C₂×#16864401	C₂²	1	1	yes	characteristic
18	#41×D₂₆₉	—	2	4	no	—
19	#41×D₂₆₉	C₂²	1	8	yes	—
20	C₂²×Dic₅₃₈	—	2	1	no	—
21	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×Q₈×D₂₆₉	—	2	1	no	—
23	C₂×Q₈×D₂₆₉	—	2	4	no	—
24	C₂×Q₈×D₂₆₉	—	2	1	no	—
25	C₂×Q₈×D₂₆₉	C₂²	1	2	yes	—
26	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₂₆₉	C₂²	1	2	yes	complemented
28	C₂×Q₈×D₂₆₉	C₂²	1	8	yes	complemented
29	C₂×D₄×D₂₆₉	—	2	1	no	—
30	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₂₆₉	—	2	1	no	—
32	C₂²×C₄×D₂₆₉	—	2	1	no	—
33	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
34	#22575486	C₂²	1	8	yes	complemented
35	#22575485	C₂²	1	16	yes	complemented
36	#22575484	C₂²	1	8	yes	complemented
37	#22575483	C₂²	1	8	yes	complemented
38	#22575482	C₂²	1	16	yes	complemented
39	C₂×Dic₁₀₇₆	C₂²	1	2	yes	complemented
40	C₂×#16864392	C₂²	1	2	yes	complemented
41	C₂×#16864392	C₂²	1	2	yes	complemented
42	Q₁₆×D₂₆₉	C₂²	1	16	yes	complemented
43	C₂×#16864391	C₂²	1	2	yes	complemented
44	C₂×#16864390	C₂²	1	2	yes	complemented
45	C₂×#16864389	C₂²	1	2	yes	complemented
46	SD₁₆×D₂₆₉	C₂²	1	16	yes	complemented
47	C₂×#16864386	C₂²	1	1	yes	characteristic, complemented
48	C₂×#16864385	C₂²	1	2	yes	complemented
49	M₁₆×D₂₆₉	C₂²	1	8	yes	complemented
50	C₂×C₈×D₂₆₉	C₂²	1	2	yes	—
51	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
53	#137×C₂₆₉	C₂²	1	8	yes	complemented
54	C₂×Q₁₆×C₂₆₉	C₂²	1	2	yes	complemented
55	C₂×SD₁₆×C₂₆₉	C₂²	1	2	yes	complemented
56	C₂×M₁₆×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
57	C₂³×D₂₆₉	—	2	1	no	—
58	C₂³×D₂₆₉	D₄	1	1	yes	characteristic
59	#16864403	—	2	2	no	—
60	#16864403	C₂³	1	4	yes	—
61	#16864402	—	2	8	no	—
62	#16864402	—	2	2	no	—
63	#16864402	C₂³	1	4	yes	—
64	#16864401	—	2	8	no	—
65	#16864401	—	2	2	no	—
66	#16864401	C₂³	1	4	yes	—
67	C₂×Dic₅₃₈	—	2	2	no	—
68	C₂×Dic₅₃₈	—	2	2	no	—
69	C₂×Dic₅₃₈	—	2	8	no	—
70	C₂×Dic₅₃₈	—	2	1	no	—
71	C₂×Dic₅₃₈	—	2	1	no	—
72	C₂×Dic₅₃₈	—	2	2	no	—
73	C₂×Dic₅₃₈	C₂³	1	2	yes	—
74	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
75	C₂×Dic₅₃₈	C₂³	1	4	yes	complemented
76	Q₈×D₂₆₉	—	2	4	no	—
77	Q₈×D₂₆₉	—	2	4	no	—
78	Q₈×D₂₆₉	—	2	8	no	—
79	Q₈×D₂₆₉	—	2	8	no	—
80	Q₈×D₂₆₉	—	2	2	no	—
81	Q₈×D₂₆₉	C₂³	1	8	yes	—
82	Q₈×D₂₆₉	C₂³	1	4	yes	—
83	Q₈×D₂₆₉	C₂³	1	8	yes	complemented
84	C₂×D₁₀₇₆	—	2	1	no	—
85	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊D₂₆₉	—	2	1	no	—
87	C₂×C₂²⋊D₂₆₉	—	2	1	no	—
88	C₂×C₂²⋊D₂₆₉	—	2	1	no	—
89	D₄×D₂₆₉	—	2	8	no	—
90	D₄×D₂₆₉	—	2	2	no	—
91	D₄×D₂₆₉	C₂³	1	4	yes	—
92	C₂²×Dic₂₆₉	—	2	1	no	—
93	C₂²×Dic₂₆₉	—	2	1	no	—
94	C₂²×Dic₂₆₉	D₄	1	1	yes	characteristic
95	C₂×C₄×D₂₆₉	—	2	1	no	—
96	C₂×C₄×D₂₆₉	—	2	2	no	—
97	C₂×C₄×D₂₆₉	—	2	2	no	—
98	C₂×C₄×D₂₆₉	—	2	8	no	—
99	C₂×C₄×D₂₆₉	—	2	1	no	—
100	C₂×C₄×D₂₆₉	—	2	8	no	—
101	C₂×C₄×D₂₆₉	—	2	1	no	—
102	C₂×C₄×D₂₆₉	D₄	1	1	yes	characteristic
103	C₂×C₄×D₂₆₉	D₄	1	4	yes	—
104	C₂×C₄×D₂₆₉	D₄	1	1	yes	characteristic
105	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
107	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
108	Dic₁₀₇₆	C₂³	1	8	yes	complemented
109	#16864392	C₂³	1	8	yes	complemented
110	#16864392	C₂³	1	8	yes	complemented
111	#16864391	C₂³	1	8	yes	complemented
112	#16864390	C₂³	1	8	yes	complemented
113	#16864389	C₂³	1	8	yes	complemented
114	#16864386	C₂³	1	4	yes	complemented
115	#16864385	C₂³	1	8	yes	complemented
116	C₂×#14524130	C₂³	1	2	yes	—
117	C₈×D₂₆₉	C₂³	1	8	yes	—
118	#41×C₂₆₉	—	2	2	no	—
119	#41×C₂₆₉	C₂³	1	4	yes	—
120	C₂×Q₈×C₂₆₉	—	2	1	no	—
121	C₂×Q₈×C₂₆₉	—	2	2	no	—
122	C₂×Q₈×C₂₆₉	C₂³	1	2	yes	—
123	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₂₆₉	C₂³	1	4	yes	complemented
125	C₂×D₄×C₂₆₉	—	2	1	no	—
126	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₂₆₉	—	2	1	no	—
128	C₂²×C₄×C₂₆₉	—	2	1	no	—
129	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
130	Q₁₆×C₂₆₉	C₂³	1	8	yes	complemented
131	SD₁₆×C₂₆₉	C₂³	1	8	yes	complemented
132	M₁₆×C₂₆₉	C₂³	1	4	yes	complemented
133	C₂×C₈×C₂₆₉	C₂³	1	2	yes	—
134	C₂²×D₂₆₉	—	2	4	no	—
135	C₂²×D₂₆₉	—	2	1	no	—
136	C₂²×D₂₆₉	—	2	4	no	—
137	C₂²×D₂₆₉	—	4	4	no	—
138	C₂²×D₂₆₉	C₂×D₄	1	4	yes	—
139	C₂²×D₂₆₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×D₂₆₉	C₂×D₄	1	1	yes	characteristic
141	Dic₅₃₈	—	2	2	no	—
142	Dic₅₃₈	—	2	4	no	—
143	Dic₅₃₈	—	2	1	no	—
144	Dic₅₃₈	—	2	8	no	—
145	Dic₅₃₈	—	2	8	no	—
146	Dic₅₃₈	—	2	4	no	—
147	Dic₅₃₈	C₂⁴	1	4	yes	—
148	Dic₅₃₈	C₂⁴	1	2	yes	—
149	D₁₀₇₆	—	2	4	no	—
150	D₁₀₇₆	—	2	1	no	—
151	D₁₀₇₆	C₂⁴	1	2	yes	—
152	C₂²⋊D₂₆₉	—	2	4	no	—
153	C₂²⋊D₂₆₉	—	2	4	no	—
154	C₂²⋊D₂₆₉	—	2	4	no	—
155	C₂×Dic₂₆₉	—	2	1	no	—
156	C₂×Dic₂₆₉	—	2	2	no	—
157	C₂×Dic₂₆₉	—	2	4	no	—
158	C₂×Dic₂₆₉	—	2	4	no	—
159	C₂×Dic₂₆₉	C₂×D₄	1	1	yes	characteristic
160	C₂×Dic₂₆₉	C₂×D₄	1	1	yes	characteristic
161	C₂×Dic₂₆₉	C₂×D₄	1	4	yes	—
162	C₄×D₂₆₉	—	2	4	no	—
163	C₄×D₂₆₉	—	2	8	no	—
164	C₄×D₂₆₉	—	2	8	no	—
165	C₄×D₂₆₉	—	2	4	no	—
166	C₄×D₂₆₉	—	2	4	no	—
167	C₄×D₂₆₉	C₂×D₄	1	4	yes	—
168	C₄×D₂₆₉	C₂×D₄	1	2	yes	—
169	C₄×D₂₆₉	C₂×D₄	1	2	yes	—
170	C₄×D₂₆₉	C₂×D₄	1	4	yes	—
171	C₄×D₂₆₉	C₂⁴	1	2	yes	—
172	C₄×D₂₆₉	C₂⁴	1	2	yes	—
173	#14524130	C₂⁴	1	4	yes	—
174	C₂³×C₂₆₉	—	2	1	no	—
175	C₂³×C₂₆₉	C₂×D₄	1	1	yes	characteristic
176	Q₈×C₂₆₉	—	2	2	no	—
177	Q₈×C₂₆₉	—	2	4	no	—
178	Q₈×C₂₆₉	—	2	1	no	—
179	Q₈×C₂₆₉	C₂⁴	1	4	yes	—
180	Q₈×C₂₆₉	C₂⁴	1	2	yes	—
181	D₄×C₂₆₉	—	2	4	no	—
182	D₄×C₂₆₉	—	2	1	no	—
183	D₄×C₂₆₉	C₂⁴	1	2	yes	—
184	C₂×C₄×C₂₆₉	—	2	1	no	—
185	C₂×C₄×C₂₆₉	—	2	2	no	—
186	C₂×C₄×C₂₆₉	—	2	4	no	—
187	C₂×C₄×C₂₆₉	—	2	4	no	—
188	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
189	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
190	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
192	C₈×C₂₆₉	C₂⁴	1	4	yes	—
193	C₂²×C₂₆₉	—	2	2	no	—
194	C₂²×C₂₆₉	—	2	2	no	—
195	C₂²×C₂₆₉	—	4	2	no	—
196	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
197	C₂²×C₂₆₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×D₂₆₉	—	2	2	no	—
199	C₂×D₂₆₉	—	2	8	no	—
200	C₂×D₂₆₉	—	2	2	no	—
201	C₂×D₂₆₉	—	4	2	no	—
202	C₂×D₂₆₉	—	4	8	no	—
203	C₂×D₂₆₉	#137	1	4	yes	direct product factor
204	C₂×D₂₆₉	C₂²×D₄	1	2	yes	—
205	C₂×D₂₆₉	C₂²×D₄	1	2	yes	—
206	C₄×C₂₆₉	—	2	2	no	—
207	C₄×C₂₆₉	—	2	4	no	—
208	C₄×C₂₆₉	C₂²×D₄	1	2	yes	—
209	C₄×C₂₆₉	C₂²×D₄	1	1	yes	characteristic
210	C₄×C₂₆₉	C₂⁵	1	1	yes	characteristic
211	Dic₂₆₉	—	2	2	no	—
212	Dic₂₆₉	—	2	4	no	—
213	Dic₂₆₉	C₂²×D₄	1	2	yes	—
214	Dic₂₆₉	C₂²×D₄	1	2	yes	—
215	C₂×C₂₆₉	—	2	2	no	—
216	C₂×C₂₆₉	—	4	2	no	—
217	C₂×C₂₆₉	C₂×#137	1	2	yes	complemented
218	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
219	D₂₆₉	—	2	2	no	—
220	D₂₆₉	—	4	2	no	—
221	D₂₆₉	C₂×#137	1	4	yes	direct product factor
222	C₂₆₉	C₂²×#137	1	1	yes	characteristic, complemented, Sylow
223	C₂²×#137	—	269	1	no	maximal, Sylow
224	C₂²×#41	—	269	1	no	—
225	C₂³×Q₈	—	269	1	no	—
226	C₂×#137	—	269	1	no	—
227	C₂×#137	—	269	1	no	—
228	C₂×#137	—	269	16	no	—
229	C₂×#137	—	269	2	no	—
230	C₂×#137	—	269	2	no	—
231	C₂×#137	—	269	1	no	—
232	C₂×#137	D₂₆₉	1	1	yes	characteristic, direct product factor
233	C₂²×Q₁₆	—	269	2	no	—
234	C₂²×SD₁₆	—	269	2	no	—
235	C₂²×M₁₆	—	269	1	no	—
236	C₂×#41	—	269	8	no	—
237	C₂×#41	—	269	1	no	—
238	C₂×#41	—	269	1	no	—
239	C₂×#41	—	269	1	no	—
240	C₂×#41	—	538	1	no	—
241	C₂×#41	—	538	1	no	—
242	C₂×#41	—	538	4	no	—
243	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic
244	C₂²×Q₈	—	269	2	no	—
245	C₂²×Q₈	—	269	1	no	—
246	C₂²×Q₈	—	269	2	no	—
247	C₂²×Q₈	—	269	8	no	—
248	C₂²×Q₈	—	269	1	no	—
249	C₂²×Q₈	—	538	1	no	—
250	C₂²×Q₈	—	538	1	no	—
251	C₂²×Q₈	—	538	4	no	—
252	C₂²×Q₈	—	538	1	no	—
253	C₂²×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
254	C₂²×D₄	—	269	1	no	—
255	C₂²×D₄	—	538	1	no	—
256	C₂³×C₄	—	269	1	no	—
257	C₂³×C₄	—	538	1	no	—
258	C₂³×C₄	—	538	1	no	—
259	#137	—	269	8	no	—
260	#137	—	269	8	no	—
261	#137	—	269	16	no	—
262	#137	—	269	16	no	—
263	#137	—	269	8	no	—
264	#137	C₂×D₂₆₉	1	8	yes	direct product factor
265	C₂×Q₁₆	—	269	2	no	—
266	C₂×Q₁₆	—	269	2	no	—
267	C₂×Q₁₆	—	269	16	no	—
268	C₂×Q₁₆	—	269	2	no	—
269	C₂×Q₁₆	C₂×D₂₆₉	1	2	yes	complemented
270	C₂×SD₁₆	—	269	2	no	—
271	C₂×SD₁₆	—	269	2	no	—
272	C₂×SD₁₆	—	269	16	no	—
273	C₂×SD₁₆	—	269	2	no	—
274	C₂×SD₁₆	C₂×D₂₆₉	1	2	yes	complemented
275	C₂×M₁₆	—	269	1	no	—
276	C₂×M₁₆	—	269	8	no	—
277	C₂×M₁₆	—	269	2	no	—
278	C₂×M₁₆	C₂×D₂₆₉	1	1	yes	characteristic, complemented
279	C₂²×C₈	—	269	2	no	—
280	C₂⁴	—	269	1	no	—
281	C₂⁴	—	538	1	no	—
282	#41	—	2	2	no	—
283	#41	—	269	4	no	—
284	#41	—	269	4	no	—
285	#41	—	269	4	no	—
286	#41	—	538	8	no	—
287	#41	—	538	8	no	—
288	#41	—	538	2	no	—
289	#41	—	538	2	no	—
290	#41	—	538	2	no	—
291	#41	C₂²×D₂₆₉	1	4	yes	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	269	8	no	—
295	C₂×Q₈	—	269	4	no	—
296	C₂×Q₈	—	269	8	no	—
297	C₂×Q₈	—	269	2	no	—
298	C₂×Q₈	—	269	1	no	—
299	C₂×Q₈	—	269	4	no	—
300	C₂×Q₈	—	538	8	no	—
301	C₂×Q₈	—	538	2	no	—
302	C₂×Q₈	—	538	2	no	—
303	C₂×Q₈	—	538	1	no	—
304	C₂×Q₈	—	538	8	no	—
305	C₂×Q₈	—	538	4	no	—
306	C₂×Q₈	—	538	4	no	—
307	C₂×Q₈	—	538	8	no	—
308	C₂×Q₈	—	538	2	no	—
309	C₂×Q₈	—	538	2	no	—
310	C₂×Q₈	—	538	1	no	—
311	C₂×Q₈	C₂²×D₂₆₉	1	2	yes	—
312	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
313	C₂×Q₈	C₂²×D₂₆₉	1	4	yes	complemented
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	269	4	no	—
316	C₂×D₄	—	269	1	no	—
317	C₂×D₄	—	538	1	no	—
318	C₂×D₄	—	538	2	no	—
319	C₂×D₄	—	538	1	no	—
320	C₂×D₄	—	538	8	no	—
321	C₂×D₄	—	538	1	no	—
322	C₂×D₄	—	538	1	no	—
323	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	269	1	no	—
327	C₂²×C₄	—	269	1	no	—
328	C₂²×C₄	—	269	4	no	—
329	C₂²×C₄	—	269	1	no	—
330	C₂²×C₄	—	269	1	no	—
331	C₂²×C₄	—	269	4	no	—
332	C₂²×C₄	—	269	1	no	—
333	C₂²×C₄	—	538	1	no	—
334	C₂²×C₄	—	538	8	no	—
335	C₂²×C₄	—	538	1	no	—
336	C₂²×C₄	—	538	8	no	—
337	C₂²×C₄	—	538	2	no	—
338	C₂²×C₄	—	538	2	no	—
339	C₂²×C₄	—	538	1	no	—
340	C₂²×C₄	—	538	1	no	—
341	C₂²×C₄	—	538	1	no	—
342	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
343	Q₁₆	—	269	8	no	—
344	Q₁₆	—	269	8	no	—
345	Q₁₆	—	269	8	no	—
346	Q₁₆	C₂²×D₂₆₉	1	8	yes	complemented
347	SD₁₆	—	269	8	no	—
348	SD₁₆	—	269	8	no	—
349	SD₁₆	—	269	8	no	—
350	SD₁₆	C₂²×D₂₆₉	1	8	yes	complemented
351	M₁₆	—	269	4	no	—
352	M₁₆	—	269	8	no	—
353	M₁₆	C₂²×D₂₆₉	1	4	yes	complemented
354	C₂×C₈	—	269	2	no	—
355	C₂×C₈	—	269	8	no	—
356	C₂×C₈	C₂²×D₂₆₉	1	2	yes	—
357	C₂³	—	2	1	no	—
358	C₂³	—	269	1	no	—
359	C₂³	—	269	4	no	—
360	C₂³	—	269	1	no	—
361	C₂³	—	538	4	no	—
362	C₂³	—	538	4	no	—
363	C₂³	—	538	1	no	—
364	C₂³	—	1076	4	no	—
365	C₂³	D₄×D₂₆₉	1	1	yes	characteristic
366	Q₈	—	2	2	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	2	1	no	—
369	Q₈	—	269	4	no	—
370	Q₈	—	269	2	no	—
371	Q₈	—	538	8	no	—
372	Q₈	—	538	8	no	—
373	Q₈	—	538	4	no	—
374	Q₈	—	538	4	no	—
375	Q₈	—	538	2	no	—
376	Q₈	—	538	1	no	—
377	Q₈	C₂³×D₂₆₉	1	4	yes	—
378	Q₈	C₂³×D₂₆₉	1	2	yes	—
379	D₄	—	2	4	no	—
380	D₄	—	2	1	no	—
381	D₄	—	269	2	no	—
382	D₄	—	538	4	no	—
383	D₄	—	538	4	no	—
384	D₄	—	538	4	no	—
385	D₄	—	538	4	no	—
386	D₄	—	538	1	no	—
387	D₄	C₂³×D₂₆₉	1	2	yes	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	269	4	no	—
393	C₂×C₄	—	269	1	no	—
394	C₂×C₄	—	269	1	no	—
395	C₂×C₄	—	269	4	no	—
396	C₂×C₄	—	269	2	no	—
397	C₂×C₄	—	269	2	no	—
398	C₂×C₄	—	269	4	no	—
399	C₂×C₄	—	269	2	no	—
400	C₂×C₄	—	269	2	no	—
401	C₂×C₄	—	538	4	no	—
402	C₂×C₄	—	538	4	no	—
403	C₂×C₄	—	538	8	no	—
404	C₂×C₄	—	538	8	no	—
405	C₂×C₄	—	538	4	no	—
406	C₂×C₄	—	538	4	no	—
407	C₂×C₄	—	538	1	no	—
408	C₂×C₄	—	538	2	no	—
409	C₂×C₄	—	538	4	no	—
410	C₂×C₄	D₄×D₂₆₉	1	2	yes	—
411	C₂×C₄	D₄×D₂₆₉	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
413	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
414	C₈	—	269	4	no	—
415	C₈	C₂³×D₂₆₉	1	4	yes	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	269	4	no	—
420	C₂²	—	269	2	no	—
421	C₂²	—	269	2	no	—
422	C₂²	—	538	8	no	—
423	C₂²	—	538	2	no	—
424	C₂²	—	538	2	no	—
425	C₂²	—	1076	8	no	—
426	C₂²	—	1076	2	no	—
427	C₂²	C₂×D₄×D₂₆₉	1	2	yes	—
428	C₂²	C₂×D₄×D₂₆₉	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	2	4	no	—
431	C₄	—	269	2	no	—
432	C₄	—	269	2	no	—
433	C₄	—	538	2	no	—
434	C₄	—	538	4	no	—
435	C₄	C₂×D₄×D₂₆₉	1	2	yes	—
436	C₄	C₂×D₄×D₂₆₉	1	1	yes	characteristic
437	C₄	C₂⁴×D₂₆₉	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	4	2	no	—
440	C₂	—	269	4	no	—
441	C₂	—	538	2	no	—
442	C₂	—	1076	2	no	—
443	C₂	#137×D₂₆₉	1	2	yes	direct product factor
444	C₂	C₂²×D₄×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₆₉
commutator, cosocle	C₄×C₂₆₉	C₂⁵
Frattini	C₄	C₂⁴×D₂₆₉
Fitting	C₂×#137×C₂₆₉	C₂
socle	C₂²×C₂₆₉	C₂²×D₄
prime radical	C₂×#41×D₂₆₉	C₂
hypercenter	C₂×#137	D₂₆₉
hypocenter	C₂₆₉	C₂²×#137
LCS	G ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#137

Complements

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

N	H ≅ G/N	type
2. C₂²×Q₈×D₂₆₉	C₂	semidirect
3. C₂×#22575486	C₂	semidirect
4. C₂×#22575485	C₂	semidirect
5. C₂×#22575484	C₂	semidirect
6. C₂×#22575483	C₂	semidirect
7. C₂×#22575482	C₂	semidirect
8. #137×D₂₆₉	C₂	direct (N × H)
9. C₂×Q₁₆×D₂₆₉	C₂	semidirect
10. C₂×SD₁₆×D₂₆₉	C₂	semidirect
11. C₂×M₁₆×D₂₆₉	C₂	semidirect
12. C₂×#137×C₂₆₉	C₂	semidirect
21. C₂²×Dic₅₃₈	C₂²	semidirect
27. C₂×Q₈×D₂₆₉	C₂²	semidirect
28. C₂×Q₈×D₂₆₉	C₂²	semidirect
34. #22575486	C₂²	semidirect
35. #22575485	C₂²	semidirect
36. #22575484	C₂²	semidirect
37. #22575483	C₂²	semidirect
38. #22575482	C₂²	semidirect
39. C₂×Dic₁₀₇₆	C₂²	semidirect
40. C₂×#16864392	C₂²	semidirect
41. C₂×#16864392	C₂²	semidirect
42. Q₁₆×D₂₆₉	C₂²	semidirect
43. C₂×#16864391	C₂²	semidirect
44. C₂×#16864390	C₂²	semidirect
45. C₂×#16864389	C₂²	semidirect
46. SD₁₆×D₂₆₉	C₂²	semidirect
47. C₂×#16864386	C₂²	semidirect
48. C₂×#16864385	C₂²	semidirect
49. M₁₆×D₂₆₉	C₂²	semidirect
52. C₂²×Q₈×C₂₆₉	C₂²	semidirect
53. #137×C₂₆₉	C₂²	semidirect
54. C₂×Q₁₆×C₂₆₉	C₂²	semidirect
55. C₂×SD₁₆×C₂₆₉	C₂²	semidirect
56. C₂×M₁₆×C₂₆₉	C₂²	semidirect
75. C₂×Dic₅₃₈	C₂³	semidirect
83. Q₈×D₂₆₉	C₂³	semidirect
108. Dic₁₀₇₆	C₂³	semidirect
109. #16864392	C₂³	semidirect
110. #16864392	C₂³	semidirect
111. #16864391	C₂³	semidirect
112. #16864390	C₂³	semidirect
113. #16864389	C₂³	semidirect
114. #16864386	C₂³	semidirect
115. #16864385	C₂³	semidirect
124. C₂×Q₈×C₂₆₉	C₂³	semidirect
130. Q₁₆×C₂₆₉	C₂³	semidirect
131. SD₁₆×C₂₆₉	C₂³	semidirect
132. M₁₆×C₂₆₉	C₂³	semidirect
203. C₂×D₂₆₉	#137	direct (N × H)
217. C₂×C₂₆₉	C₂×#137	semidirect
221. D₂₆₉	C₂×#137	direct (N × H)
222. C₂₆₉	C₂²×#137	semidirect
232. C₂×#137	D₂₆₉	direct (N × H)
253. C₂²×Q₈	C₂×D₂₆₉	semidirect
264. #137	C₂×D₂₆₉	direct (N × H)
269. C₂×Q₁₆	C₂×D₂₆₉	semidirect
274. C₂×SD₁₆	C₂×D₂₆₉	semidirect
278. C₂×M₁₆	C₂×D₂₆₉	semidirect
313. C₂×Q₈	C₂²×D₂₆₉	semidirect
346. Q₁₆	C₂²×D₂₆₉	semidirect
350. SD₁₆	C₂²×D₂₆₉	semidirect
353. M₁₆	C₂²×D₂₆₉	semidirect
443. C₂	#137×D₂₆₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#41×D₂₆₉	2
C₂²×Q₈×D₂₆₉	2
C₂×#22575486	2
C₂×#22575485	2
C₂×#22575484	2
C₂×#22575483	2
C₂×#22575482	2
#137×D₂₆₉	2
C₂×Q₁₆×D₂₆₉	2
C₂×SD₁₆×D₂₆₉	2
C₂×M₁₆×D₂₆₉	2
C₂×#137×C₂₆₉	2
C₂²×#137	269

Subgroups — C2×#137×D269 #46825621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#137×D₂₆₉ #46825621