Subgroups — C₂×#123×D₂₆₉ #46824115

Order 34432.

1968 conjugacy classes of subgroups.

The subgroup lattice has 356 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	1	yes	maximal, characteristic
2	C₂³×C₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22575438	C₂	1	2	yes	maximal, complemented
4	C₂×#22575437	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22575436	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22575435	C₂	1	2	yes	maximal, complemented
7	C₂×#22575434	C₂	1	1	yes	maximal, characteristic, complemented
8	#123×D₂₆₉	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₄⋊C₄×D₂₆₉	C₂	1	2	yes	maximal, complemented
10	C₂×C₂²⋊C₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊C₄×D₂₆₉	C₂	1	2	yes	maximal, complemented
12	C₂×#123×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₆₉	C₂²	1	1	yes	characteristic
14	C₂⁴×D₂₆₉	C₂²	1	1	yes	characteristic
15	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₂₆₉	—	2	8	no	—
19	C₂×D₄×D₂₆₉	C₂²	1	8	yes	—
20	C₂³×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄×D₂₆₉	—	2	8	no	—
22	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	—
23	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	—
25	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	complemented
26	C₂²×C₄×D₂₆₉	C₂²	1	8	yes	complemented
27	#22575438	C₂²	1	16	yes	complemented
28	#22575437	C₂²	1	8	yes	complemented
29	#22575436	C₂²	1	8	yes	complemented
30	#22575435	C₂²	1	16	yes	complemented
31	#22575434	C₂²	1	8	yes	complemented
32	C₂×C₄⋊Dic₂₆₉	C₂²	1	2	yes	complemented
33	C₂×#16864381	C₂²	1	2	yes	complemented
34	C₂×#16864381	C₂²	1	2	yes	complemented
35	C₄⋊C₄×D₂₆₉	C₂²	1	16	yes	complemented
36	C₂×C₂²⋊Dic₂₆₉	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×#16864379	C₂²	1	2	yes	complemented
39	C₂×#16864379	C₂²	1	2	yes	complemented
40	C₂×#16864379	C₂²	1	2	yes	complemented
41	C₂²⋊C₄×D₂₆₉	C₂²	1	16	yes	complemented
42	C₂²⋊C₄×D₂₆₉	C₂²	1	8	yes	complemented
43	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
44	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
45	#123×C₂₆₉	C₂²	1	8	yes	complemented
46	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
47	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
48	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
49	C₂³×D₂₆₉	—	2	8	no	—
50	C₂³×D₂₆₉	—	2	4	no	—
51	C₂³×D₂₆₉	—	2	8	no	—
52	C₂³×D₂₆₉	D₄	1	8	yes	—
53	C₂³×D₂₆₉	C₂³	1	4	yes	—
54	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
55	C₂³×D₂₆₉	C₂³	1	4	yes	—
56	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
57	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
58	C₂×D₁₀₇₆	—	2	4	no	—
59	C₂×D₁₀₇₆	C₂³	1	4	yes	—
60	C₂×C₂²⋊D₂₆₉	—	2	4	no	—
61	C₂×C₂²⋊D₂₆₉	—	2	4	no	—
62	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
63	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
64	D₄×D₂₆₉	—	2	32	no	—
65	C₂²×Dic₂₆₉	—	2	4	no	—
66	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
67	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
68	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
69	C₂²×Dic₂₆₉	C₂³	1	4	yes	complemented
70	C₂×C₄×D₂₆₉	—	2	8	no	—
71	C₂×C₄×D₂₆₉	—	2	8	no	—
72	C₂×C₄×D₂₆₉	—	2	32	no	—
73	C₂×C₄×D₂₆₉	—	2	4	no	—
74	C₂×C₄×D₂₆₉	—	2	8	no	—
75	C₂×C₄×D₂₆₉	C₂³	1	8	yes	—
76	C₂×C₄×D₂₆₉	C₂³	1	8	yes	—
77	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
78	C₂×C₄×D₂₆₉	C₂³	1	8	yes	complemented
79	C₄⋊Dic₂₆₉	C₂³	1	8	yes	complemented
80	#16864381	C₂³	1	8	yes	complemented
81	#16864381	C₂³	1	8	yes	complemented
82	C₂²⋊Dic₂₆₉	C₂³	1	8	yes	complemented
83	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	complemented
84	#16864379	C₂³	1	8	yes	complemented
85	#16864379	C₂³	1	8	yes	complemented
86	#16864379	C₂³	1	8	yes	complemented
87	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
88	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₂₆₉	—	2	4	no	—
90	C₂×D₄×C₂₆₉	C₂³	1	4	yes	—
91	C₂²×C₄×C₂₆₉	—	2	4	no	—
92	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
93	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
94	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	complemented
96	C₄⋊C₄×C₂₆₉	C₂³	1	8	yes	complemented
97	C₂²⋊C₄×C₂₆₉	C₂³	1	8	yes	complemented
98	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	complemented
99	C₂²×D₂₆₉	—	2	4	no	—
100	C₂²×D₂₆₉	—	2	32	no	—
101	C₂²×D₂₆₉	—	2	16	no	—
102	C₂²×D₂₆₉	—	2	2	no	—
103	C₂²×D₂₆₉	—	2	4	no	—
104	C₂²×D₂₆₉	—	2	8	no	—
105	C₂²×D₂₆₉	—	2	16	no	—
106	C₂²×D₂₆₉	—	4	16	no	—
107	C₂²×D₂₆₉	C₂×D₄	1	16	yes	—
108	C₂²×D₂₆₉	C₂×D₄	1	4	yes	—
109	C₂²×D₂₆₉	C₂×D₄	1	4	yes	—
110	C₂²×D₂₆₉	#41	1	8	yes	—
111	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
112	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
113	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
114	D₁₀₇₆	—	2	8	no	—
115	C₂²⋊D₂₆₉	—	2	8	no	—
116	C₂²⋊D₂₆₉	—	2	8	no	—
117	C₂×Dic₂₆₉	—	2	4	no	—
118	C₂×Dic₂₆₉	—	2	8	no	—
119	C₂×Dic₂₆₉	—	2	2	no	—
120	C₂×Dic₂₆₉	—	2	4	no	—
121	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
122	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
123	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
124	C₄×D₂₆₉	—	2	16	no	—
125	C₄×D₂₆₉	—	2	16	no	—
126	C₄×D₂₆₉	—	2	8	no	—
127	C₄×D₂₆₉	—	2	16	no	—
128	C₂³×C₂₆₉	—	2	4	no	—
129	C₂³×C₂₆₉	—	2	2	no	—
130	C₂³×C₂₆₉	—	2	4	no	—
131	C₂³×C₂₆₉	C₂×D₄	1	4	yes	—
132	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
133	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
134	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
135	D₄×C₂₆₉	—	2	8	no	—
136	C₂×C₄×C₂₆₉	—	2	4	no	—
137	C₂×C₄×C₂₆₉	—	2	8	no	—
138	C₂×C₄×C₂₆₉	—	2	2	no	—
139	C₂×C₄×C₂₆₉	—	2	4	no	—
140	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
141	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
142	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
143	C₂²×C₂₆₉	—	2	8	no	—
144	C₂²×C₂₆₉	—	2	4	no	—
145	C₂²×C₂₆₉	—	2	2	no	—
146	C₂²×C₂₆₉	—	2	4	no	—
147	C₂²×C₂₆₉	—	4	4	no	—
148	C₂²×C₂₆₉	C₂²×D₄	1	4	yes	—
149	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
150	C₂²×C₂₆₉	C₂×#41	1	4	yes	—
151	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
152	C₂×D₂₆₉	—	2	8	no	—
153	C₂×D₂₆₉	—	2	4	no	—
154	C₂×D₂₆₉	—	2	32	no	—
155	C₂×D₂₆₉	—	2	2	no	—
156	C₂×D₂₆₉	—	2	4	no	—
157	C₂×D₂₆₉	—	4	4	no	—
158	C₂×D₂₆₉	—	4	16	no	—
159	C₂×D₂₆₉	#123	1	16	yes	direct product factor
160	C₂×D₂₆₉	C₂²×D₄	1	4	yes	—
161	C₂×D₂₆₉	C₂²×D₄	1	4	yes	—
162	C₂×D₂₆₉	C₂×#41	1	8	yes	—
163	C₄×C₂₆₉	—	2	4	no	—
164	C₄×C₂₆₉	—	2	2	no	—
165	C₄×C₂₆₉	—	2	4	no	—
166	Dic₂₆₉	—	2	4	no	—
167	Dic₂₆₉	—	2	2	no	—
168	Dic₂₆₉	—	2	4	no	—
169	C₂×C₂₆₉	—	2	4	no	—
170	C₂×C₂₆₉	—	4	2	no	—
171	C₂×C₂₆₉	C₂×#123	1	4	yes	complemented
172	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
173	C₂×C₂₆₉	C₂²×#41	1	2	yes	—
174	D₂₆₉	—	2	4	no	—
175	D₂₆₉	—	4	2	no	—
176	D₂₆₉	C₂×#123	1	8	yes	direct product factor
177	C₂₆₉	C₂²×#123	1	1	yes	characteristic, complemented, Sylow
178	C₂²×#123	—	269	1	no	maximal, Sylow
179	C₂³×D₄	—	269	1	no	—
180	C₂⁴×C₄	—	269	1	no	—
181	C₂×#123	—	269	1	no	—
182	C₂×#123	—	269	1	no	—
183	C₂×#123	—	269	16	no	—
184	C₂×#123	—	269	2	no	—
185	C₂×#123	—	269	2	no	—
186	C₂×#123	—	269	1	no	—
187	C₂×#123	D₂₆₉	1	1	yes	characteristic, direct product factor
188	C₂²×C₄⋊C₄	—	269	2	no	—
189	C₂²×C₂²⋊C₄	—	269	1	no	—
190	C₂²×C₂²⋊C₄	—	269	2	no	—
191	C₂⁵	—	269	1	no	—
192	C₂⁵	—	269	1	no	—
193	C₂²×D₄	—	269	1	no	—
194	C₂²×D₄	—	269	1	no	—
195	C₂²×D₄	—	269	8	no	—
196	C₂²×D₄	—	269	1	no	—
197	C₂²×D₄	—	538	8	no	—
198	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic
199	C₂³×C₄	—	269	1	no	—
200	C₂³×C₄	—	269	2	no	—
201	C₂³×C₄	—	269	2	no	—
202	C₂³×C₄	—	269	1	no	—
203	C₂³×C₄	—	269	2	no	—
204	C₂³×C₄	—	269	8	no	—
205	C₂³×C₄	—	538	8	no	—
206	C₂³×C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
207	#123	—	269	8	no	—
208	#123	—	269	8	no	—
209	#123	—	269	16	no	—
210	#123	—	269	16	no	—
211	#123	—	269	8	no	—
212	#123	C₂×D₂₆₉	1	8	yes	direct product factor
213	C₂×C₄⋊C₄	—	269	2	no	—
214	C₂×C₄⋊C₄	—	269	2	no	—
215	C₂×C₄⋊C₄	—	269	2	no	—
216	C₂×C₄⋊C₄	—	269	16	no	—
217	C₂×C₄⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
218	C₂×C₂²⋊C₄	—	269	1	no	—
219	C₂×C₂²⋊C₄	—	269	2	no	—
220	C₂×C₂²⋊C₄	—	269	2	no	—
221	C₂×C₂²⋊C₄	—	269	2	no	—
222	C₂×C₂²⋊C₄	—	269	2	no	—
223	C₂×C₂²⋊C₄	—	269	8	no	—
224	C₂×C₂²⋊C₄	—	269	16	no	—
225	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
226	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
227	C₂⁴	—	269	1	no	—
228	C₂⁴	—	269	8	no	—
229	C₂⁴	—	269	4	no	—
230	C₂⁴	—	269	1	no	—
231	C₂⁴	—	269	4	no	—
232	C₂⁴	—	269	1	no	—
233	C₂⁴	—	538	8	no	—
234	C₂⁴	—	538	4	no	—
235	C₂⁴	—	538	8	no	—
236	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
237	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	269	4	no	—
240	C₂×D₄	—	269	4	no	—
241	C₂×D₄	—	269	4	no	—
242	C₂×D₄	—	538	4	no	—
243	C₂×D₄	—	538	32	no	—
244	C₂×D₄	—	538	4	no	—
245	C₂×D₄	—	538	4	no	—
246	C₂×D₄	C₂²×D₂₆₉	1	4	yes	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	269	4	no	—
249	C₂²×C₄	—	269	2	no	—
250	C₂²×C₄	—	269	2	no	—
251	C₂²×C₄	—	269	1	no	—
252	C₂²×C₄	—	269	8	no	—
253	C₂²×C₄	—	269	8	no	—
254	C₂²×C₄	—	269	4	no	—
255	C₂²×C₄	—	269	8	no	—
256	C₂²×C₄	—	538	8	no	—
257	C₂²×C₄	—	538	8	no	—
258	C₂²×C₄	—	538	32	no	—
259	C₂²×C₄	—	538	8	no	—
260	C₂²×C₄	—	538	4	no	—
261	C₂²×C₄	—	538	4	no	—
262	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
263	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
264	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²×D₂₆₉	1	4	yes	complemented
266	C₄⋊C₄	—	269	8	no	—
267	C₄⋊C₄	—	269	8	no	—
268	C₄⋊C₄	—	269	8	no	—
269	C₄⋊C₄	C₂²×D₂₆₉	1	8	yes	complemented
270	C₂²⋊C₄	—	269	4	no	—
271	C₂²⋊C₄	—	269	8	no	—
272	C₂²⋊C₄	—	269	8	no	—
273	C₂²⋊C₄	—	269	8	no	—
274	C₂²⋊C₄	—	269	8	no	—
275	C₂²⋊C₄	C₂²×D₂₆₉	1	4	yes	complemented
276	C₂²⋊C₄	C₂²×D₂₆₉	1	8	yes	complemented
277	C₂³	—	2	4	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	269	4	no	—
281	C₂³	—	269	8	no	—
282	C₂³	—	269	2	no	—
283	C₂³	—	269	16	no	—
284	C₂³	—	269	4	no	—
285	C₂³	—	269	2	no	—
286	C₂³	—	269	2	no	—
287	C₂³	—	538	16	no	—
288	C₂³	—	538	32	no	—
289	C₂³	—	538	8	no	—
290	C₂³	—	538	16	no	—
291	C₂³	—	538	4	no	—
292	C₂³	—	538	2	no	—
293	C₂³	—	538	4	no	—
294	C₂³	—	1076	16	no	—
295	C₂³	D₄×D₂₆₉	1	4	yes	—
296	C₂³	C₂³×D₂₆₉	1	2	yes	—
297	C₂³	C₂³×D₂₆₉	1	2	yes	—
298	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
299	D₄	—	2	8	no	—
300	D₄	—	538	8	no	—
301	D₄	—	538	8	no	—
302	D₄	—	538	8	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	269	4	no	—
308	C₂×C₄	—	269	4	no	—
309	C₂×C₄	—	269	2	no	—
310	C₂×C₄	—	538	16	no	—
311	C₂×C₄	—	538	16	no	—
312	C₂×C₄	—	538	8	no	—
313	C₂×C₄	—	538	16	no	—
314	C₂×C₄	—	538	8	no	—
315	C₂×C₄	—	538	4	no	—
316	C₂×C₄	—	538	2	no	—
317	C₂×C₄	—	538	4	no	—
318	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
319	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
320	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	269	4	no	—
327	C₂²	—	269	8	no	—
328	C₂²	—	269	16	no	—
329	C₂²	—	269	4	no	—
330	C₂²	—	538	32	no	—
331	C₂²	—	538	4	no	—
332	C₂²	—	538	8	no	—
333	C₂²	—	538	2	no	—
334	C₂²	—	538	4	no	—
335	C₂²	—	1076	16	no	—
336	C₂²	—	1076	4	no	—
337	C₂²	C₂×D₄×D₂₆₉	1	4	yes	—
338	C₂²	C₂×D₄×D₂₆₉	1	2	yes	—
339	C₂²	#41×D₂₆₉	1	4	yes	—
340	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	4	no	—
344	C₄	—	538	4	no	—
345	C₄	—	538	2	no	—
346	C₄	—	538	4	no	—
347	C₂	—	2	4	no	—
348	C₂	—	4	2	no	—
349	C₂	—	269	8	no	—
350	C₂	—	538	4	no	—
351	C₂	—	1076	2	no	—
352	C₂	#123×D₂₆₉	1	4	yes	direct product factor
353	C₂	C₂²×D₄×D₂₆₉	1	1	yes	characteristic
354	C₂	C₂×#41×D₂₆₉	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₂₆₉
commutator, cosocle	C₂²×C₂₆₉	C₂⁵
Frattini	C₂²	C₂⁴×D₂₆₉
Fitting	C₂×#123×C₂₆₉	C₂
socle	C₂³×C₂₆₉	C₂⁴
prime radical	C₂²×D₄×D₂₆₉	C₂
hypercenter	C₂×#123	D₂₆₉
hypocenter	C₂₆₉	C₂²×#123
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂³ ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×D₂₆₉	C₂	semidirect
3. C₂×#22575438	C₂	semidirect
4. C₂×#22575437	C₂	semidirect
5. C₂×#22575436	C₂	semidirect
6. C₂×#22575435	C₂	semidirect
7. C₂×#22575434	C₂	semidirect
8. #123×D₂₆₉	C₂	direct (N × H)
9. C₂×C₄⋊C₄×D₂₆₉	C₂	semidirect
10. C₂×C₂²⋊C₄×D₂₆₉	C₂	semidirect
11. C₂×C₂²⋊C₄×D₂₆₉	C₂	semidirect
12. C₂×#123×C₂₆₉	C₂	semidirect
20. C₂³×Dic₂₆₉	C₂²	semidirect
25. C₂²×C₄×D₂₆₉	C₂²	semidirect
26. C₂²×C₄×D₂₆₉	C₂²	semidirect
27. #22575438	C₂²	semidirect
28. #22575437	C₂²	semidirect
29. #22575436	C₂²	semidirect
30. #22575435	C₂²	semidirect
31. #22575434	C₂²	semidirect
32. C₂×C₄⋊Dic₂₆₉	C₂²	semidirect
33. C₂×#16864381	C₂²	semidirect
34. C₂×#16864381	C₂²	semidirect
35. C₄⋊C₄×D₂₆₉	C₂²	semidirect
36. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
37. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
38. C₂×#16864379	C₂²	semidirect
39. C₂×#16864379	C₂²	semidirect
40. C₂×#16864379	C₂²	semidirect
41. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
42. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
44. C₂³×C₄×C₂₆₉	C₂²	semidirect
45. #123×C₂₆₉	C₂²	semidirect
46. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
47. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
69. C₂²×Dic₂₆₉	C₂³	semidirect
78. C₂×C₄×D₂₆₉	C₂³	semidirect
79. C₄⋊Dic₂₆₉	C₂³	semidirect
80. #16864381	C₂³	semidirect
81. #16864381	C₂³	semidirect
82. C₂²⋊Dic₂₆₉	C₂³	semidirect
83. C₂²⋊Dic₂₆₉	C₂³	semidirect
84. #16864379	C₂³	semidirect
85. #16864379	C₂³	semidirect
86. #16864379	C₂³	semidirect
95. C₂²×C₄×C₂₆₉	C₂³	semidirect
96. C₄⋊C₄×C₂₆₉	C₂³	semidirect
97. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
98. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
159. C₂×D₂₆₉	#123	direct (N × H)
171. C₂×C₂₆₉	C₂×#123	semidirect
176. D₂₆₉	C₂×#123	direct (N × H)
177. C₂₆₉	C₂²×#123	semidirect
187. C₂×#123	D₂₆₉	direct (N × H)
206. C₂³×C₄	C₂×D₂₆₉	semidirect
212. #123	C₂×D₂₆₉	direct (N × H)
217. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
225. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
226. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
265. C₂²×C₄	C₂²×D₂₆₉	semidirect
269. C₄⋊C₄	C₂²×D₂₆₉	semidirect
275. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
276. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
352. C₂	#123×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×#22575438	2
C₂×#22575437	2
C₂×#22575436	2
C₂×#22575435	2
C₂×#22575434	2
#123×D₂₆₉	2
C₂×C₄⋊C₄×D₂₆₉	2
C₂×C₂²⋊C₄×D₂₆₉	2
C₂×#123×C₂₆₉	2
C₂²×#123	269

Subgroups — C2×#123×D269 #46824115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#123×D₂₆₉ #46824115