Subgroups — C₂×#31771404 #46825631

Order 34432.

1484 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16864403	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771404	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22575485	C₂	1	2	yes	maximal, complemented
5	C₂×#22575484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22575481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22575480	C₂	1	2	yes	maximal, complemented
8	C₂×#22575478	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#22575476	C₂	1	2	yes	maximal, complemented
10	C₂×#22575474	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	—	2	1	no	—
14	C₂×#16864403	—	2	1	no	—
15	C₂×#16864403	—	2	4	no	—
16	C₂×#16864403	C₂²	1	2	yes	—
17	C₂×#16864403	C₂²	1	1	yes	characteristic, complemented
18	C₂×#16864403	C₂²	1	2	yes	complemented
19	C₂×#16864403	C₂²	1	8	yes	complemented
20	C₂×#16864402	—	2	1	no	—
21	C₂×#16864402	C₂²	1	1	yes	characteristic
22	C₂×#16864401	—	2	1	no	—
23	C₂×#16864401	C₂²	1	1	yes	characteristic, complemented
24	#41×D₂₆₉	—	2	4	no	—
25	#41×D₂₆₉	C₂²	1	8	yes	complemented
26	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₁₀₇₆	—	2	1	no	—
28	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₂₆₉	—	2	1	no	—
30	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×D₂₆₉	—	2	1	no	—
32	C₂²×C₄×D₂₆₉	—	2	1	no	—
33	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
34	#22575485	C₂²	1	16	yes	complemented
35	#22575484	C₂²	1	8	yes	complemented
36	#22575481	C₂²	1	8	yes	complemented
37	#22575480	C₂²	1	16	yes	complemented
38	#22575478	C₂²	1	8	yes	complemented
39	#22575476	C₂²	1	16	yes	complemented
40	#22575474	C₂²	1	16	yes	complemented
41	C₂×#16864392	C₂²	1	2	yes	complemented
42	C₂×#16864391	C₂²	1	2	yes	complemented
43	C₂×#16864389	C₂²	1	2	yes	complemented
44	C₂×#16864389	C₂²	1	2	yes	complemented
45	C₂×D₂₁₅₂	C₂²	1	2	yes	complemented
46	C₂×#16864387	C₂²	1	2	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	complemented
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	—	2	1	no	—
59	C₂³×D₂₆₉	D₄	1	1	yes	characteristic
60	#16864403	—	2	2	no	—
61	#16864403	—	2	4	no	—
62	#16864403	—	2	4	no	—
63	#16864403	—	2	8	no	—
64	#16864403	—	2	8	no	—
65	#16864403	C₂³	1	8	yes	—
66	#16864403	C₂³	1	8	yes	complemented
67	#16864403	C₂³	1	4	yes	complemented
68	#16864402	—	2	8	no	—
69	#16864402	—	2	2	no	—
70	#16864402	C₂³	1	4	yes	—
71	#16864401	—	2	8	no	—
72	#16864401	—	2	2	no	—
73	#16864401	C₂³	1	4	yes	complemented
74	C₂×Dic₅₃₈	—	2	1	no	—
75	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
76	Q₈×D₂₆₉	—	2	2	no	—
77	Q₈×D₂₆₉	C₂³	1	4	yes	complemented
78	C₂×D₁₀₇₆	—	2	1	no	—
79	C₂×D₁₀₇₆	—	2	2	no	—
80	C₂×D₁₀₇₆	—	2	2	no	—
81	C₂×D₁₀₇₆	—	2	8	no	—
82	C₂×D₁₀₇₆	—	2	1	no	—
83	C₂×D₁₀₇₆	—	2	2	no	—
84	C₂×D₁₀₇₆	C₂³	1	2	yes	—
85	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
86	C₂×D₁₀₇₆	C₂³	1	4	yes	complemented
87	C₂×C₂²⋊D₂₆₉	—	2	1	no	—
88	C₂×C₂²⋊D₂₆₉	—	2	1	no	—
89	C₂×C₂²⋊D₂₆₉	—	2	1	no	—
90	D₄×D₂₆₉	—	2	8	no	—
91	D₄×D₂₆₉	—	2	2	no	—
92	D₄×D₂₆₉	C₂³	1	4	yes	complemented
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	1	no	—
97	C₂×C₄×D₂₆₉	—	2	2	no	—
98	C₂×C₄×D₂₆₉	—	2	2	no	—
99	C₂×C₄×D₂₆₉	—	2	8	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	#16864392	C₂³	1	8	yes	complemented
109	#16864391	C₂³	1	8	yes	complemented
110	#16864389	C₂³	1	8	yes	complemented
111	#16864389	C₂³	1	8	yes	complemented
112	D₂₁₅₂	C₂³	1	8	yes	complemented
113	#16864387	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	complemented
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	1	yes	characteristic
123	C₂×Q₈×C₂₆₉	C₂³	1	2	yes	—
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	1	no	—
135	C₂²×D₂₆₉	—	2	2	no	—
136	C₂²×D₂₆₉	—	2	4	no	—
137	C₂²×D₂₆₉	—	2	4	no	—
138	C₂²×D₂₆₉	—	4	2	no	—
139	C₂²×D₂₆₉	—	4	4	no	—
140	C₂²×D₂₆₉	—	4	4	no	—
141	C₂²×D₂₆₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×D₂₆₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×D₂₆₉	C₂×D₄	1	4	yes	—
144	Dic₅₃₈	—	2	1	no	—
145	Dic₅₃₈	—	2	4	no	—
146	Dic₅₃₈	C₂⁴	1	2	yes	—
147	D₁₀₇₆	—	2	4	no	—
148	D₁₀₇₆	—	2	8	no	—
149	D₁₀₇₆	—	2	8	no	—
150	D₁₀₇₆	—	2	1	no	—
151	D₁₀₇₆	—	2	2	no	—
152	D₁₀₇₆	—	2	4	no	—
153	D₁₀₇₆	C₂⁴	1	4	yes	—
154	D₁₀₇₆	C₂⁴	1	2	yes	—
155	C₂²⋊D₂₆₉	—	2	4	no	—
156	C₂²⋊D₂₆₉	—	2	4	no	—
157	C₂²⋊D₂₆₉	—	2	4	no	—
158	C₂×Dic₂₆₉	—	2	1	no	—
159	C₂×Dic₂₆₉	—	2	4	no	—
160	C₂×Dic₂₆₉	C₂×D₄	1	1	yes	characteristic
161	C₂×Dic₂₆₉	C₂×D₄	1	1	yes	characteristic
162	C₂×Dic₂₆₉	C₂×D₄	1	4	yes	—
163	C₄×D₂₆₉	—	2	4	no	—
164	C₄×D₂₆₉	—	2	4	no	—
165	C₄×D₂₆₉	—	2	4	no	—
166	C₄×D₂₆₉	—	2	8	no	—
167	C₄×D₂₆₉	—	2	8	no	—
168	C₄×D₂₆₉	C₂×D₄	1	4	yes	—
169	C₄×D₂₆₉	C₂×D₄	1	2	yes	—
170	C₄×D₂₆₉	C₂×D₄	1	2	yes	—
171	C₄×D₂₆₉	C₂×D₄	1	4	yes	—
172	C₄×D₂₆₉	C₂⁴	1	2	yes	—
173	C₄×D₂₆₉	C₂⁴	1	2	yes	—
174	#14524130	C₂⁴	1	4	yes	—
175	C₂³×C₂₆₉	—	2	1	no	—
176	C₂³×C₂₆₉	C₂×D₄	1	1	yes	characteristic
177	Q₈×C₂₆₉	—	2	2	no	—
178	Q₈×C₂₆₉	—	2	4	no	—
179	Q₈×C₂₆₉	—	2	1	no	—
180	Q₈×C₂₆₉	C₂⁴	1	4	yes	—
181	Q₈×C₂₆₉	C₂⁴	1	2	yes	—
182	D₄×C₂₆₉	—	2	4	no	—
183	D₄×C₂₆₉	—	2	1	no	—
184	D₄×C₂₆₉	C₂⁴	1	2	yes	—
185	C₂×C₄×C₂₆₉	—	2	1	no	—
186	C₂×C₄×C₂₆₉	—	2	2	no	—
187	C₂×C₄×C₂₆₉	—	2	4	no	—
188	C₂×C₄×C₂₆₉	—	2	4	no	—
189	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
190	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
191	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
193	C₈×C₂₆₉	C₂⁴	1	4	yes	—
194	C₂²×C₂₆₉	—	2	2	no	—
195	C₂²×C₂₆₉	—	2	2	no	—
196	C₂²×C₂₆₉	—	4	2	no	—
197	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
198	C₂²×C₂₆₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×D₂₆₉	—	2	2	no	—
200	C₂×D₂₆₉	—	2	2	no	—
201	C₂×D₂₆₉	—	2	2	no	—
202	C₂×D₂₆₉	—	2	4	no	—
203	C₂×D₂₆₉	—	4	4	no	—
204	C₂×D₂₆₉	—	4	8	no	—
205	C₂×D₂₆₉	—	4	8	no	—
206	C₂×D₂₆₉	—	4	2	no	—
207	C₂×D₂₆₉	—	4	4	no	—
208	C₂×D₂₆₉	C₂²×D₄	1	2	yes	—
209	C₂×D₂₆₉	C₂²×D₄	1	2	yes	—
210	C₄×C₂₆₉	—	2	2	no	—
211	C₄×C₂₆₉	—	2	4	no	—
212	C₄×C₂₆₉	C₂²×D₄	1	2	yes	—
213	C₄×C₂₆₉	C₂²×D₄	1	1	yes	characteristic
214	C₄×C₂₆₉	C₂⁵	1	1	yes	characteristic
215	Dic₂₆₉	—	2	2	no	—
216	Dic₂₆₉	C₂²×D₄	1	2	yes	—
217	Dic₂₆₉	C₂²×D₄	1	2	yes	—
218	C₂×C₂₆₉	—	2	2	no	—
219	C₂×C₂₆₉	—	4	2	no	—
220	C₂×C₂₆₉	#575	1	2	yes	complemented
221	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
222	D₂₆₉	—	2	2	no	—
223	D₂₆₉	—	2	2	no	—
224	D₂₆₉	—	4	2	no	—
225	D₂₆₉	—	4	4	no	—
226	C₂₆₉	C₂×#575	1	1	yes	characteristic, complemented, Sylow
227	C₂×#575	—	269	1	no	maximal, Sylow
228	C₂²×#41	—	269	1	no	—
229	C₂²×#41	—	269	1	no	—
230	#575	—	269	16	no	—
231	C₂×#137	—	269	1	no	—
232	C₂×#137	—	269	2	no	—
233	C₂×#137	D₂₆₉	1	1	yes	characteristic, complemented
234	C₂×AGL(1,ℤ/8)	—	269	1	no	—
235	C₂×AGL(1,ℤ/8)	—	269	2	no	—
236	C₂×AGL(1,ℤ/8)	—	269	1	no	—
237	C₂×#135	—	269	2	no	—
238	C₂×#135	—	269	2	no	—
239	C₂²×M₁₆	—	269	1	no	—
240	C₂×#41	—	269	8	no	—
241	C₂×#41	—	269	1	no	—
242	C₂×#41	—	269	2	no	—
243	C₂×#41	—	269	2	no	—
244	C₂×#41	—	269	8	no	—
245	C₂×#41	—	269	1	no	—
246	C₂×#41	—	269	1	no	—
247	C₂×#41	—	538	1	no	—
248	C₂×#41	—	538	1	no	—
249	C₂×#41	—	538	1	no	—
250	C₂×#41	—	538	4	no	—
251	C₂×#41	—	538	1	no	—
252	C₂×#41	—	538	4	no	—
253	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic
254	C₂²×Q₈	—	269	1	no	—
255	C₂²×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
256	C₂²×D₄	—	269	1	no	—
257	C₂²×D₄	—	269	1	no	—
258	C₂²×D₄	—	538	1	no	—
259	C₂²×D₄	—	538	1	no	—
260	C₂³×C₄	—	269	1	no	—
261	C₂³×C₄	—	538	1	no	—
262	C₂³×C₄	—	538	1	no	—
263	#137	—	269	8	no	—
264	#137	—	269	16	no	—
265	#137	C₂×D₂₆₉	1	8	yes	complemented
266	AGL(1,ℤ/8)	—	269	8	no	—
267	AGL(1,ℤ/8)	—	269	16	no	—
268	AGL(1,ℤ/8)	—	269	8	no	—
269	#135	—	269	16	no	—
270	#135	—	269	16	no	—
271	C₂×Q₁₆	—	269	2	no	—
272	C₂×Q₁₆	C₂×D₂₆₉	1	2	yes	complemented
273	C₂×SD₁₆	—	269	2	no	—
274	C₂×SD₁₆	—	269	2	no	—
275	C₂×SD₁₆	—	269	2	no	—
276	C₂×SD₁₆	C₂×D₂₆₉	1	2	yes	complemented
277	C₂×D₈	—	269	2	no	—
278	C₂×D₈	—	269	2	no	—
279	C₂×M₁₆	—	269	1	no	—
280	C₂×M₁₆	—	269	8	no	—
281	C₂×M₁₆	—	269	2	no	—
282	C₂×M₁₆	C₂×D₂₆₉	1	1	yes	characteristic, complemented
283	C₂²×C₈	—	269	2	no	—
284	C₂⁴	—	269	1	no	—
285	C₂⁴	—	538	1	no	—
286	C₂⁴	—	538	1	no	—
287	#41	—	2	2	no	—
288	#41	—	269	4	no	—
289	#41	—	269	8	no	—
290	#41	—	269	8	no	—
291	#41	—	269	4	no	—
292	#41	—	269	4	no	—
293	#41	—	538	8	no	—
294	#41	—	538	8	no	—
295	#41	—	538	2	no	—
296	#41	—	538	8	no	—
297	#41	—	538	4	no	—
298	#41	—	538	4	no	—
299	#41	—	538	8	no	—
300	#41	—	538	2	no	—
301	#41	—	538	2	no	—
302	#41	C₂²×D₂₆₉	1	4	yes	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	269	4	no	—
306	C₂×Q₈	—	269	1	no	—
307	C₂×Q₈	—	538	1	no	—
308	C₂×Q₈	—	538	2	no	—
309	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
310	C₂×Q₈	C₂²×D₂₆₉	1	2	yes	—
311	C₂×Q₈	C₂²×D₂₆₉	1	4	yes	complemented
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	269	4	no	—
314	C₂×D₄	—	269	2	no	—
315	C₂×D₄	—	269	1	no	—
316	C₂×D₄	—	269	4	no	—
317	C₂×D₄	—	538	8	no	—
318	C₂×D₄	—	538	1	no	—
319	C₂×D₄	—	538	2	no	—
320	C₂×D₄	—	538	2	no	—
321	C₂×D₄	—	538	2	no	—
322	C₂×D₄	—	538	1	no	—
323	C₂×D₄	—	538	8	no	—
324	C₂×D₄	—	538	1	no	—
325	C₂×D₄	—	538	1	no	—
326	C₂×D₄	—	538	2	no	—
327	C₂×D₄	—	538	1	no	—
328	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	269	1	no	—
332	C₂²×C₄	—	269	1	no	—
333	C₂²×C₄	—	269	4	no	—
334	C₂²×C₄	—	269	1	no	—
335	C₂²×C₄	—	269	1	no	—
336	C₂²×C₄	—	269	1	no	—
337	C₂²×C₄	—	269	4	no	—
338	C₂²×C₄	—	538	8	no	—
339	C₂²×C₄	—	538	1	no	—
340	C₂²×C₄	—	538	2	no	—
341	C₂²×C₄	—	538	2	no	—
342	C₂²×C₄	—	538	8	no	—
343	C₂²×C₄	—	538	1	no	—
344	C₂²×C₄	—	538	1	no	—
345	C₂²×C₄	—	538	1	no	—
346	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
347	Q₁₆	—	269	8	no	—
348	Q₁₆	C₂²×D₂₆₉	1	8	yes	complemented
349	SD₁₆	—	269	8	no	—
350	SD₁₆	—	269	8	no	—
351	SD₁₆	—	269	8	no	—
352	SD₁₆	C₂²×D₂₆₉	1	8	yes	complemented
353	D₈	—	269	8	no	—
354	D₈	—	269	8	no	—
355	M₁₆	—	269	4	no	—
356	M₁₆	—	269	8	no	—
357	M₁₆	C₂²×D₂₆₉	1	4	yes	complemented
358	C₂×C₈	—	269	2	no	—
359	C₂×C₈	—	269	8	no	—
360	C₂×C₈	C₂²×D₂₆₉	1	2	yes	—
361	C₂³	—	2	1	no	—
362	C₂³	—	269	1	no	—
363	C₂³	—	269	1	no	—
364	C₂³	—	269	4	no	—
365	C₂³	—	538	4	no	—
366	C₂³	—	538	4	no	—
367	C₂³	—	538	2	no	—
368	C₂³	—	538	1	no	—
369	C₂³	—	1076	2	no	—
370	C₂³	—	1076	4	no	—
371	C₂³	—	1076	4	no	—
372	C₂³	D₄×D₂₆₉	1	1	yes	characteristic
373	Q₈	—	2	2	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	269	2	no	—
377	Q₈	—	538	4	no	—
378	Q₈	—	538	1	no	—
379	Q₈	C₂³×D₂₆₉	1	2	yes	—
380	Q₈	C₂³×D₂₆₉	1	4	yes	—
381	D₄	—	2	4	no	—
382	D₄	—	2	1	no	—
383	D₄	—	269	4	no	—
384	D₄	—	269	2	no	—
385	D₄	—	538	4	no	—
386	D₄	—	538	8	no	—
387	D₄	—	538	8	no	—
388	D₄	—	538	4	no	—
389	D₄	—	538	4	no	—
390	D₄	—	538	4	no	—
391	D₄	—	538	4	no	—
392	D₄	—	538	1	no	—
393	D₄	—	538	2	no	—
394	D₄	C₂³×D₂₆₉	1	2	yes	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	269	4	no	—
400	C₂×C₄	—	269	1	no	—
401	C₂×C₄	—	269	1	no	—
402	C₂×C₄	—	269	4	no	—
403	C₂×C₄	—	269	2	no	—
404	C₂×C₄	—	269	2	no	—
405	C₂×C₄	—	269	4	no	—
406	C₂×C₄	—	269	2	no	—
407	C₂×C₄	—	269	2	no	—
408	C₂×C₄	—	538	4	no	—
409	C₂×C₄	—	538	8	no	—
410	C₂×C₄	—	538	8	no	—
411	C₂×C₄	—	538	4	no	—
412	C₂×C₄	—	538	4	no	—
413	C₂×C₄	—	538	1	no	—
414	C₂×C₄	—	538	4	no	—
415	C₂×C₄	D₄×D₂₆₉	1	2	yes	—
416	C₂×C₄	D₄×D₂₆₉	1	1	yes	characteristic
417	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
418	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
419	C₈	—	269	4	no	—
420	C₈	C₂³×D₂₆₉	1	4	yes	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	269	2	no	—
425	C₂²	—	269	2	no	—
426	C₂²	—	538	2	no	—
427	C₂²	—	538	2	no	—
428	C₂²	—	538	4	no	—
429	C₂²	—	538	2	no	—
430	C₂²	—	1076	4	no	—
431	C₂²	—	1076	8	no	—
432	C₂²	—	1076	8	no	—
433	C₂²	—	1076	4	no	—
434	C₂²	—	1076	2	no	—
435	C₂²	C₂×D₄×D₂₆₉	1	2	yes	—
436	C₂²	C₂×D₄×D₂₆₉	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	269	2	no	—
440	C₄	—	269	2	no	—
441	C₄	—	538	2	no	—
442	C₄	C₂×D₄×D₂₆₉	1	2	yes	—
443	C₄	C₂×D₄×D₂₆₉	1	1	yes	characteristic
444	C₄	C₂⁴×D₂₆₉	1	1	yes	characteristic
445	C₂	—	2	2	no	—
446	C₂	—	4	2	no	—
447	C₂	—	538	2	no	—
448	C₂	—	538	2	no	—
449	C₂	—	1076	4	no	—
450	C₂	—	1076	2	no	—
451	C₂	#31771404	1	2	yes	direct product factor
452	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
hypercenter	C₂×#137	D₂₆₉
hypocenter	C₂₆₉	C₂×#575
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
1. C₂²×#16864403	C₂	semidirect
2. C₂×#41×D₂₆₉	C₂	semidirect
3. #31771404	C₂	direct (N × H)
4. C₂×#22575485	C₂	semidirect
5. C₂×#22575484	C₂	semidirect
6. C₂×#22575481	C₂	semidirect
7. C₂×#22575480	C₂	semidirect
8. C₂×#22575478	C₂	semidirect
9. C₂×#22575476	C₂	semidirect
10. C₂×#22575474	C₂	semidirect
11. C₂×M₁₆×D₂₆₉	C₂	semidirect
12. C₂×#137×C₂₆₉	C₂	semidirect
17. C₂×#16864403	C₂²	semidirect
18. C₂×#16864403	C₂²	semidirect
19. C₂×#16864403	C₂²	semidirect
23. C₂×#16864401	C₂²	semidirect
25. #41×D₂₆₉	C₂²	semidirect
26. C₂×Q₈×D₂₆₉	C₂²	semidirect
28. C₂²×D₁₀₇₆	C₂²	semidirect
30. C₂×D₄×D₂₆₉	C₂²	semidirect
34. #22575485	C₂²	semidirect
35. #22575484	C₂²	semidirect
36. #22575481	C₂²	semidirect
37. #22575480	C₂²	semidirect
38. #22575478	C₂²	semidirect
39. #22575476	C₂²	semidirect
40. #22575474	C₂²	semidirect
41. C₂×#16864392	C₂²	semidirect
42. C₂×#16864391	C₂²	semidirect
43. C₂×#16864389	C₂²	semidirect
44. C₂×#16864389	C₂²	semidirect
45. C₂×D₂₁₅₂	C₂²	semidirect
46. C₂×#16864387	C₂²	semidirect
47. C₂×#16864386	C₂²	semidirect
48. C₂×#16864385	C₂²	semidirect
49. M₁₆×D₂₆₉	C₂²	semidirect
50. C₂×C₈×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
66. #16864403	C₂³	semidirect
67. #16864403	C₂³	semidirect
73. #16864401	C₂³	semidirect
77. Q₈×D₂₆₉	C₂³	semidirect
86. C₂×D₁₀₇₆	C₂³	semidirect
92. D₄×D₂₆₉	C₂³	semidirect
108. #16864392	C₂³	semidirect
109. #16864391	C₂³	semidirect
110. #16864389	C₂³	semidirect
111. #16864389	C₂³	semidirect
112. D₂₁₅₂	C₂³	semidirect
113. #16864387	C₂³	semidirect
114. #16864386	C₂³	semidirect
115. #16864385	C₂³	semidirect
117. C₈×D₂₆₉	C₂³	semidirect
124. C₂×Q₈×C₂₆₉	C₂³	semidirect
130. Q₁₆×C₂₆₉	C₂³	semidirect
131. SD₁₆×C₂₆₉	C₂³	semidirect
132. M₁₆×C₂₆₉	C₂³	semidirect
220. C₂×C₂₆₉	#575	semidirect
226. C₂₆₉	C₂×#575	semidirect
233. C₂×#137	D₂₆₉	semidirect
255. C₂²×Q₈	C₂×D₂₆₉	semidirect
265. #137	C₂×D₂₆₉	semidirect
272. C₂×Q₁₆	C₂×D₂₆₉	semidirect
276. C₂×SD₁₆	C₂×D₂₆₉	semidirect
282. C₂×M₁₆	C₂×D₂₆₉	semidirect
311. C₂×Q₈	C₂²×D₂₆₉	semidirect
348. Q₁₆	C₂²×D₂₆₉	semidirect
352. SD₁₆	C₂²×D₂₆₉	semidirect
357. M₁₆	C₂²×D₂₆₉	semidirect
451. C₂	#31771404	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#16864403	2
C₂×#41×D₂₆₉	2
#31771404	2
C₂×#22575485	2
C₂×#22575484	2
C₂×#22575481	2
C₂×#22575480	2
C₂×#22575478	2
C₂×#22575476	2
C₂×#22575474	2
C₂×M₁₆×D₂₆₉	2
C₂×#137×C₂₆₉	2
C₂×#575	269

Subgroups — C2×#31771404 #46825631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31771404 #46825631