Subgroups — C₂×#121×D₂₆₉ #46824103

Order 34432.

2528 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₂₆₉	C₂	1	2	yes	maximal, complemented
2	C₂²×D₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#22575428	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22575427	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22575426	C₂	1	2	yes	maximal, complemented
7	C₂×#22575425	C₂	1	2	yes	maximal, complemented
8	C₂×#22575424	C₂	1	1	yes	maximal, characteristic, complemented
9	#121×D₂₆₉	C₂	1	16	yes	maximal, direct product factor
10	C₂×C₄⋊C₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊C₄×D₂₆₉	C₂	1	2	yes	maximal, complemented
12	C₂×#121×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₆₉	C₂²	1	2	yes	—
14	C₂⁴×D₂₆₉	C₂²	1	1	yes	characteristic
15	C₂²×D₁₀₇₆	C₂²	1	2	yes	complemented
16	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
20	C₂×D₄×D₂₆₉	—	2	16	no	—
21	C₂×D₄×D₂₆₉	—	2	8	no	—
22	C₂×D₄×D₂₆₉	C₂²	1	8	yes	complemented
23	C₂×D₄×D₂₆₉	C₂²	1	16	yes	complemented
24	C₂³×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×D₂₆₉	—	2	8	no	—
26	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	—
28	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×D₂₆₉	C₂²	1	8	yes	complemented
32	#22575428	C₂²	1	8	yes	complemented
33	#22575427	C₂²	1	8	yes	complemented
34	#22575426	C₂²	1	16	yes	complemented
35	#22575425	C₂²	1	16	yes	complemented
36	#22575424	C₂²	1	8	yes	complemented
37	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×#16864381	C₂²	1	2	yes	complemented
39	C₄⋊C₄×D₂₆₉	C₂²	1	8	yes	complemented
40	C₂×C₂²⋊Dic₂₆₉	C₂²	1	2	yes	complemented
41	C₂×#16864379	C₂²	1	2	yes	complemented
42	C₂×#16864379	C₂²	1	2	yes	complemented
43	C₂²⋊C₄×D₂₆₉	C₂²	1	16	yes	complemented
44	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₄×C₂₆₉	C₂²	1	2	yes	complemented
46	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
47	#121×C₂₆₉	C₂²	1	8	yes	complemented
48	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
50	C₂³×D₂₆₉	—	2	4	no	—
51	C₂³×D₂₆₉	—	2	4	no	—
52	C₂³×D₂₆₉	—	2	8	no	—
53	C₂³×D₂₆₉	—	2	8	no	—
54	C₂³×D₂₆₉	—	2	8	no	—
55	C₂³×D₂₆₉	D₄	1	8	yes	complemented
56	C₂³×D₂₆₉	C₂³	1	8	yes	—
57	C₂³×D₂₆₉	C₂³	1	2	yes	—
58	C₂³×D₂₆₉	C₂³	1	4	yes	—
59	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
60	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
61	C₂×D₁₀₇₆	—	2	8	no	—
62	C₂×D₁₀₇₆	—	2	4	no	—
63	C₂×D₁₀₇₆	C₂³	1	8	yes	complemented
64	C₂×D₁₀₇₆	C₂³	1	4	yes	complemented
65	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
66	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
67	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
68	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
69	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
70	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
71	D₄×D₂₆₉	—	2	64	no	—
72	D₄×D₂₆₉	—	2	32	no	—
73	C₂²×Dic₂₆₉	—	2	4	no	—
74	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
75	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
76	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
77	C₂²×Dic₂₆₉	C₂³	1	4	yes	complemented
78	C₂×C₄×D₂₆₉	—	2	4	no	—
79	C₂×C₄×D₂₆₉	—	2	8	no	—
80	C₂×C₄×D₂₆₉	—	2	4	no	—
81	C₂×C₄×D₂₆₉	—	2	32	no	—
82	C₂×C₄×D₂₆₉	—	2	4	no	—
83	C₂×C₄×D₂₆₉	D₄	1	8	yes	complemented
84	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
85	C₂×C₄×D₂₆₉	C₂³	1	8	yes	—
86	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
87	C₂×C₄×D₂₆₉	C₂³	1	4	yes	complemented
88	C₂×C₄×D₂₆₉	C₂³	1	4	yes	complemented
89	C₄⋊Dic₂₆₉	C₂³	1	4	yes	complemented
90	#16864381	C₂³	1	8	yes	complemented
91	C₂²⋊Dic₂₆₉	C₂³	1	8	yes	complemented
92	#16864379	C₂³	1	8	yes	complemented
93	#16864379	C₂³	1	8	yes	complemented
94	C₂⁴×C₂₆₉	C₂³	1	2	yes	—
95	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
96	C₂×D₄×C₂₆₉	—	2	8	no	—
97	C₂×D₄×C₂₆₉	—	2	4	no	—
98	C₂×D₄×C₂₆₉	C₂³	1	4	yes	complemented
99	C₂×D₄×C₂₆₉	C₂³	1	8	yes	complemented
100	C₂²×C₄×C₂₆₉	—	2	4	no	—
101	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
103	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	complemented
105	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	complemented
106	C₂²⋊C₄×C₂₆₉	C₂³	1	8	yes	complemented
107	C₂²×D₂₆₉	—	2	2	no	—
108	C₂²×D₂₆₉	—	2	2	no	—
109	C₂²×D₂₆₉	—	2	32	no	—
110	C₂²×D₂₆₉	—	2	8	no	—
111	C₂²×D₂₆₉	—	2	8	no	—
112	C₂²×D₂₆₉	—	2	4	no	—
113	C₂²×D₂₆₉	—	2	4	no	—
114	C₂²×D₂₆₉	—	2	4	no	—
115	C₂²×D₂₆₉	—	2	16	no	—
116	C₂²×D₂₆₉	—	2	16	no	—
117	C₂²×D₂₆₉	—	2	16	no	—
118	C₂²×D₂₆₉	—	4	32	no	—
119	C₂²×D₂₆₉	C₂×D₄	1	4	yes	—
120	C₂²×D₂₆₉	C₂×D₄	1	4	yes	—
121	C₂²×D₂₆₉	C₂×D₄	1	16	yes	complemented
122	C₂²×D₂₆₉	C₂×D₄	1	4	yes	complemented
123	C₂²×D₂₆₉	#41	1	4	yes	—
124	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
125	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
126	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
127	D₁₀₇₆	—	2	16	no	—
128	D₁₀₇₆	—	2	8	no	—
129	C₂²⋊D₂₆₉	—	2	16	no	—
130	C₂²⋊D₂₆₉	—	2	16	no	—
131	C₂²⋊D₂₆₉	—	2	16	no	—
132	C₂×Dic₂₆₉	—	2	2	no	—
133	C₂×Dic₂₆₉	—	2	4	no	—
134	C₂×Dic₂₆₉	—	2	8	no	—
135	C₂×Dic₂₆₉	C₂×D₄	1	4	yes	complemented
136	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
137	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
138	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
139	C₄×D₂₆₉	—	2	8	no	—
140	C₄×D₂₆₉	—	2	16	no	—
141	C₄×D₂₆₉	—	2	8	no	—
142	C₄×D₂₆₉	—	2	8	no	—
143	C₄×D₂₆₉	C₂×D₄	1	16	yes	complemented
144	C₂³×C₂₆₉	—	2	2	no	—
145	C₂³×C₂₆₉	—	2	2	no	—
146	C₂³×C₂₆₉	—	2	4	no	—
147	C₂³×C₂₆₉	—	2	4	no	—
148	C₂³×C₂₆₉	—	2	4	no	—
149	C₂³×C₂₆₉	C₂×D₄	1	4	yes	complemented
150	C₂³×C₂₆₉	C₂⁴	1	4	yes	—
151	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
152	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
153	D₄×C₂₆₉	—	2	16	no	—
154	D₄×C₂₆₉	—	2	8	no	—
155	C₂×C₄×C₂₆₉	—	2	2	no	—
156	C₂×C₄×C₂₆₉	—	2	4	no	—
157	C₂×C₄×C₂₆₉	—	2	8	no	—
158	C₂×C₄×C₂₆₉	C₂×D₄	1	4	yes	complemented
159	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
160	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
161	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
162	C₂²×C₂₆₉	—	2	8	no	—
163	C₂²×C₂₆₉	—	2	2	no	—
164	C₂²×C₂₆₉	—	2	2	no	—
165	C₂²×C₂₆₉	—	2	4	no	—
166	C₂²×C₂₆₉	—	2	4	no	—
167	C₂²×C₂₆₉	—	2	4	no	—
168	C₂²×C₂₆₉	—	4	8	no	—
169	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
170	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
171	C₂²×C₂₆₉	C₂²×D₄	1	4	yes	complemented
172	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
173	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
174	C₂×D₂₆₉	—	2	8	no	—
175	C₂×D₂₆₉	—	2	2	no	—
176	C₂×D₂₆₉	—	2	2	no	—
177	C₂×D₂₆₉	—	2	32	no	—
178	C₂×D₂₆₉	—	2	4	no	—
179	C₂×D₂₆₉	—	2	4	no	—
180	C₂×D₂₆₉	—	2	4	no	—
181	C₂×D₂₆₉	—	4	8	no	—
182	C₂×D₂₆₉	—	4	32	no	—
183	C₂×D₂₆₉	#121	1	16	yes	direct product factor
184	C₂×D₂₆₉	C₂²×D₄	1	4	yes	—
185	C₂×D₂₆₉	C₂²×D₄	1	4	yes	—
186	C₂×D₂₆₉	C₂²×D₄	1	4	yes	complemented
187	C₂×D₂₆₉	C₂×#41	1	4	yes	—
188	C₄×C₂₆₉	—	2	2	no	—
189	C₄×C₂₆₉	—	2	4	no	—
190	C₄×C₂₆₉	C₂²×D₄	1	4	yes	complemented
191	Dic₂₆₉	—	2	2	no	—
192	Dic₂₆₉	—	2	4	no	—
193	Dic₂₆₉	C₂²×D₄	1	4	yes	complemented
194	C₂×C₂₆₉	—	2	4	no	—
195	C₂×C₂₆₉	—	4	4	no	—
196	C₂×C₂₆₉	C₂×#121	1	4	yes	complemented
197	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
198	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
199	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
200	D₂₆₉	—	2	4	no	—
201	D₂₆₉	—	4	4	no	—
202	D₂₆₉	C₂×#121	1	8	yes	direct product factor
203	C₂₆₉	C₂²×#121	1	1	yes	characteristic, complemented, Sylow
204	C₂²×#121	—	269	1	no	maximal, Sylow
205	C₂³×D₄	—	269	1	no	—
206	C₂³×D₄	—	269	2	no	—
207	C₂⁴×C₄	—	269	1	no	—
208	C₂×#121	—	269	1	no	—
209	C₂×#121	—	269	2	no	—
210	C₂×#121	—	269	1	no	—
211	C₂×#121	—	269	16	no	—
212	C₂×#121	—	269	1	no	—
213	C₂×#121	—	269	2	no	—
214	C₂×#121	D₂₆₉	1	1	yes	characteristic, direct product factor
215	C₂²×C₄⋊C₄	—	269	1	no	—
216	C₂²×C₂²⋊C₄	—	269	2	no	—
217	C₂⁵	—	269	1	no	—
218	C₂⁵	—	269	2	no	—
219	C₂²×D₄	—	269	2	no	—
220	C₂²×D₄	—	269	2	no	—
221	C₂²×D₄	—	269	2	no	—
222	C₂²×D₄	—	269	8	no	—
223	C₂²×D₄	—	269	16	no	—
224	C₂²×D₄	—	269	2	no	—
225	C₂²×D₄	—	269	1	no	—
226	C₂²×D₄	—	538	8	no	—
227	C₂²×D₄	—	538	16	no	—
228	C₂²×D₄	C₂×D₂₆₉	1	2	yes	complemented
229	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
230	C₂³×C₄	—	269	1	no	—
231	C₂³×C₄	—	269	1	no	—
232	C₂³×C₄	—	269	1	no	—
233	C₂³×C₄	—	269	2	no	—
234	C₂³×C₄	—	269	1	no	—
235	C₂³×C₄	—	269	1	no	—
236	C₂³×C₄	—	269	8	no	—
237	C₂³×C₄	—	538	8	no	—
238	C₂³×C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
239	#121	—	269	8	no	—
240	#121	—	269	16	no	—
241	#121	—	269	8	no	—
242	#121	—	269	8	no	—
243	#121	—	269	16	no	—
244	#121	C₂×D₂₆₉	1	8	yes	direct product factor
245	C₂×C₄⋊C₄	—	269	2	no	—
246	C₂×C₄⋊C₄	—	269	1	no	—
247	C₂×C₄⋊C₄	—	269	8	no	—
248	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
249	C₂×C₂²⋊C₄	—	269	2	no	—
250	C₂×C₂²⋊C₄	—	269	2	no	—
251	C₂×C₂²⋊C₄	—	269	2	no	—
252	C₂×C₂²⋊C₄	—	269	16	no	—
253	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
254	C₂⁴	—	269	1	no	—
255	C₂⁴	—	269	8	no	—
256	C₂⁴	—	269	4	no	—
257	C₂⁴	—	269	1	no	—
258	C₂⁴	—	269	8	no	—
259	C₂⁴	—	269	2	no	—
260	C₂⁴	—	538	4	no	—
261	C₂⁴	—	538	4	no	—
262	C₂⁴	—	538	8	no	—
263	C₂⁴	—	538	8	no	—
264	C₂⁴	—	538	8	no	—
265	C₂⁴	C₂²×D₂₆₉	1	2	yes	—
266	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	269	8	no	—
270	C₂×D₄	—	269	8	no	—
271	C₂×D₄	—	269	8	no	—
272	C₂×D₄	—	269	8	no	—
273	C₂×D₄	—	269	4	no	—
274	C₂×D₄	—	538	8	no	—
275	C₂×D₄	—	538	32	no	—
276	C₂×D₄	—	538	8	no	—
277	C₂×D₄	—	538	64	no	—
278	C₂×D₄	—	538	8	no	—
279	C₂×D₄	—	538	8	no	—
280	C₂×D₄	—	538	4	no	—
281	C₂×D₄	C₂²×D₂₆₉	1	8	yes	complemented
282	C₂×D₄	C₂²×D₂₆₉	1	4	yes	complemented
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	269	1	no	—
285	C₂²×C₄	—	269	8	no	—
286	C₂²×C₄	—	269	4	no	—
287	C₂²×C₄	—	269	4	no	—
288	C₂²×C₄	—	269	1	no	—
289	C₂²×C₄	—	269	2	no	—
290	C₂²×C₄	—	269	4	no	—
291	C₂²×C₄	—	269	8	no	—
292	C₂²×C₄	—	269	4	no	—
293	C₂²×C₄	—	269	4	no	—
294	C₂²×C₄	—	538	4	no	—
295	C₂²×C₄	—	538	32	no	—
296	C₂²×C₄	—	538	4	no	—
297	C₂²×C₄	—	538	8	no	—
298	C₂²×C₄	—	538	4	no	—
299	C₂²×C₄	—	538	4	no	—
300	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
302	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₂₆₉	1	4	yes	complemented
304	C₄⋊C₄	—	269	8	no	—
305	C₄⋊C₄	—	269	4	no	—
306	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	complemented
307	C₂²⋊C₄	—	269	8	no	—
308	C₂²⋊C₄	—	269	8	no	—
309	C₂²⋊C₄	—	269	8	no	—
310	C₂²⋊C₄	C₂²×D₂₆₉	1	8	yes	complemented
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	269	4	no	—
317	C₂³	—	269	4	no	—
318	C₂³	—	269	4	no	—
319	C₂³	—	269	2	no	—
320	C₂³	—	269	4	no	—
321	C₂³	—	269	16	no	—
322	C₂³	—	269	2	no	—
323	C₂³	—	269	4	no	—
324	C₂³	—	538	8	no	—
325	C₂³	—	538	8	no	—
326	C₂³	—	538	32	no	—
327	C₂³	—	538	16	no	—
328	C₂³	—	538	16	no	—
329	C₂³	—	538	16	no	—
330	C₂³	—	538	2	no	—
331	C₂³	—	538	2	no	—
332	C₂³	—	538	4	no	—
333	C₂³	—	538	4	no	—
334	C₂³	—	538	4	no	—
335	C₂³	—	1076	32	no	—
336	C₂³	D₄×D₂₆₉	1	4	yes	complemented
337	C₂³	C₂³×D₂₆₉	1	4	yes	—
338	C₂³	C₂³×D₂₆₉	1	2	yes	—
339	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
340	D₄	—	2	16	no	—
341	D₄	—	2	8	no	—
342	D₄	—	538	16	no	—
343	D₄	—	538	16	no	—
344	D₄	—	538	16	no	—
345	D₄	—	538	16	no	—
346	D₄	—	538	8	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	269	4	no	—
351	C₂×C₄	—	269	2	no	—
352	C₂×C₄	—	269	16	no	—
353	C₂×C₄	—	269	2	no	—
354	C₂×C₄	—	269	4	no	—
355	C₂×C₄	—	538	8	no	—
356	C₂×C₄	—	538	8	no	—
357	C₂×C₄	—	538	16	no	—
358	C₂×C₄	—	538	8	no	—
359	C₂×C₄	—	538	2	no	—
360	C₂×C₄	—	538	4	no	—
361	C₂×C₄	—	538	8	no	—
362	C₂×C₄	D₄×D₂₆₉	1	4	yes	complemented
363	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
364	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
365	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	8	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	269	4	no	—
374	C₂²	—	269	4	no	—
375	C₂²	—	269	4	no	—
376	C₂²	—	269	16	no	—
377	C₂²	—	269	4	no	—
378	C₂²	—	538	32	no	—
379	C₂²	—	538	2	no	—
380	C₂²	—	538	2	no	—
381	C₂²	—	538	8	no	—
382	C₂²	—	538	4	no	—
383	C₂²	—	538	4	no	—
384	C₂²	—	538	4	no	—
385	C₂²	—	1076	32	no	—
386	C₂²	—	1076	8	no	—
387	C₂²	C₂×D₄×D₂₆₉	1	2	yes	—
388	C₂²	C₂×D₄×D₂₆₉	1	2	yes	—
389	C₂²	C₂×D₄×D₂₆₉	1	4	yes	complemented
390	C₂²	#41×D₂₆₉	1	2	yes	—
391	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	2	4	no	—
394	C₄	—	269	4	no	—
395	C₄	—	538	2	no	—
396	C₄	—	538	4	no	—
397	C₄	C₂×D₄×D₂₆₉	1	4	yes	complemented
398	C₂	—	2	4	no	—
399	C₂	—	4	4	no	—
400	C₂	—	269	8	no	—
401	C₂	—	538	4	no	—
402	C₂	—	1076	4	no	—
403	C₂	#121×D₂₆₉	1	4	yes	direct product factor
404	C₂	C₂²×D₄×D₂₆₉	1	1	yes	characteristic
405	C₂	C₂²×D₄×D₂₆₉	1	1	yes	characteristic
406	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₆₉
commutator, cosocle	C₂²×C₂₆₉	C₂⁵
Frattini	C₂²	C₂⁴×D₂₆₉
Fitting	C₂×#121×C₂₆₉	C₂
socle	C₂³×C₂₆₉	C₂⁴
hypercenter	C₂×#121	D₂₆₉
hypocenter	C₂₆₉	C₂²×#121
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₂₆₉	C₂	semidirect
2. C₂²×D₄×D₂₆₉	C₂	semidirect
3. C₂³×C₄×D₂₆₉	C₂	semidirect
4. C₂×#22575428	C₂	semidirect
5. C₂×#22575427	C₂	semidirect
6. C₂×#22575426	C₂	semidirect
7. C₂×#22575425	C₂	semidirect
8. C₂×#22575424	C₂	semidirect
9. #121×D₂₆₉	C₂	direct (N × H)
10. C₂×C₄⋊C₄×D₂₆₉	C₂	semidirect
11. C₂×C₂²⋊C₄×D₂₆₉	C₂	semidirect
12. C₂×#121×C₂₆₉	C₂	semidirect
15. C₂²×D₁₀₇₆	C₂²	semidirect
16. C₂²×D₁₀₇₆	C₂²	semidirect
17. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
18. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
19. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
22. C₂×D₄×D₂₆₉	C₂²	semidirect
23. C₂×D₄×D₂₆₉	C₂²	semidirect
24. C₂³×Dic₂₆₉	C₂²	semidirect
29. C₂²×C₄×D₂₆₉	C₂²	semidirect
30. C₂²×C₄×D₂₆₉	C₂²	semidirect
31. C₂²×C₄×D₂₆₉	C₂²	semidirect
32. #22575428	C₂²	semidirect
33. #22575427	C₂²	semidirect
34. #22575426	C₂²	semidirect
35. #22575425	C₂²	semidirect
36. #22575424	C₂²	semidirect
37. C₂×C₄⋊Dic₂₆₉	C₂²	semidirect
38. C₂×#16864381	C₂²	semidirect
39. C₄⋊C₄×D₂₆₉	C₂²	semidirect
40. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
41. C₂×#16864379	C₂²	semidirect
42. C₂×#16864379	C₂²	semidirect
43. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
44. C₂²×D₄×C₂₆₉	C₂²	semidirect
45. C₂²×D₄×C₂₆₉	C₂²	semidirect
46. C₂³×C₄×C₂₆₉	C₂²	semidirect
47. #121×C₂₆₉	C₂²	semidirect
48. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
49. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
55. C₂³×D₂₆₉	D₄	semidirect
63. C₂×D₁₀₇₆	C₂³	semidirect
64. C₂×D₁₀₇₆	C₂³	semidirect
68. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
69. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
70. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
77. C₂²×Dic₂₆₉	C₂³	semidirect
83. C₂×C₄×D₂₆₉	D₄	semidirect
87. C₂×C₄×D₂₆₉	C₂³	semidirect
88. C₂×C₄×D₂₆₉	C₂³	semidirect
89. C₄⋊Dic₂₆₉	C₂³	semidirect
90. #16864381	C₂³	semidirect
91. C₂²⋊Dic₂₆₉	C₂³	semidirect
92. #16864379	C₂³	semidirect
93. #16864379	C₂³	semidirect
98. C₂×D₄×C₂₆₉	C₂³	semidirect
99. C₂×D₄×C₂₆₉	C₂³	semidirect
104. C₂²×C₄×C₂₆₉	C₂³	semidirect
105. C₄⋊C₄×C₂₆₉	C₂³	semidirect
106. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
121. C₂²×D₂₆₉	C₂×D₄	semidirect
122. C₂²×D₂₆₉	C₂×D₄	semidirect
135. C₂×Dic₂₆₉	C₂×D₄	semidirect
143. C₄×D₂₆₉	C₂×D₄	semidirect
149. C₂³×C₂₆₉	C₂×D₄	semidirect
158. C₂×C₄×C₂₆₉	C₂×D₄	semidirect
171. C₂²×C₂₆₉	C₂²×D₄	semidirect
183. C₂×D₂₆₉	#121	direct (N × H)
186. C₂×D₂₆₉	C₂²×D₄	semidirect
190. C₄×C₂₆₉	C₂²×D₄	semidirect
193. Dic₂₆₉	C₂²×D₄	semidirect
196. C₂×C₂₆₉	C₂×#121	semidirect
202. D₂₆₉	C₂×#121	direct (N × H)
203. C₂₆₉	C₂²×#121	semidirect
214. C₂×#121	D₂₆₉	direct (N × H)
228. C₂²×D₄	C₂×D₂₆₉	semidirect
229. C₂²×D₄	C₂×D₂₆₉	semidirect
238. C₂³×C₄	C₂×D₂₆₉	semidirect
244. #121	C₂×D₂₆₉	direct (N × H)
248. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
253. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
281. C₂×D₄	C₂²×D₂₆₉	semidirect
282. C₂×D₄	C₂²×D₂₆₉	semidirect
303. C₂²×C₄	C₂²×D₂₆₉	semidirect
306. C₄⋊C₄	C₂²×D₂₆₉	semidirect
310. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
336. C₂³	D₄×D₂₆₉	semidirect
362. C₂×C₄	D₄×D₂₆₉	semidirect
389. C₂²	C₂×D₄×D₂₆₉	semidirect
397. C₄	C₂×D₄×D₂₆₉	semidirect
403. C₂	#121×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
C₂²×D₄×D₂₆₉	2
C₂³×C₄×D₂₆₉	2
C₂×#22575428	2
C₂×#22575427	2
C₂×#22575426	2
C₂×#22575425	2
C₂×#22575424	2
#121×D₂₆₉	2
C₂×C₄⋊C₄×D₂₆₉	2
C₂×C₂²⋊C₄×D₂₆₉	2
C₂×#121×C₂₆₉	2
C₂²×#121	269

Subgroups — C2×#121×D269 #46824103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#121×D₂₆₉ #46824103