Subgroups — C₂×#31771237 #46824321

Order 34432.

2536 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	C₂³×C₂²⋊D₂₆₉	C₂	1	2	yes	maximal, complemented
2	C₂²×D₄×D₂₆₉	C₂	1	2	yes	maximal, complemented
3	#31771237	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22575449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22575426	C₂	1	2	yes	maximal, complemented
6	C₂×#22575425	C₂	1	2	yes	maximal, complemented
7	C₂×#22575423	C₂	1	2	yes	maximal, complemented
8	C₂×#22575421	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#22575413	C₂	1	2	yes	maximal, complemented
10	C₂×#120×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁴×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
12	C₂⁴×D₂₆₉	C₂²	1	2	yes	complemented
13	C₂²×D₁₀₇₆	C₂²	1	2	yes	complemented
14	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊D₂₆₉	—	2	16	no	—
16	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
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	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₂₆₉	C₂²	1	16	yes	complemented
22	C₂×D₄×D₂₆₉	—	2	16	no	—
23	C₂×D₄×D₂₆₉	C₂²	1	16	yes	complemented
24	C₂³×Dic₂₆₉	C₂²	1	2	yes	complemented
25	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	complemented
26	#22575449	C₂²	1	8	yes	complemented
27	#22575426	C₂²	1	16	yes	complemented
28	#22575425	C₂²	1	16	yes	complemented
29	#22575423	C₂²	1	16	yes	complemented
30	#22575421	C₂²	1	8	yes	complemented
31	#22575413	C₂²	1	16	yes	complemented
32	C₂×#16864381	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#16864379	C₂²	1	2	yes	complemented
35	C₂×#16864379	C₂²	1	2	yes	complemented
36	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
37	C₂⁵×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₄×C₂₆₉	C₂²	1	2	yes	complemented
39	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
40	#120×C₂₆₉	C₂²	1	8	yes	complemented
41	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
43	C₂³×D₂₆₉	—	2	8	no	—
44	C₂³×D₂₆₉	—	2	8	no	—
45	C₂³×D₂₆₉	—	2	8	no	—
46	C₂³×D₂₆₉	—	4	4	no	—
47	C₂³×D₂₆₉	—	4	2	no	—
48	C₂³×D₂₆₉	C₂³	1	2	yes	—
49	C₂³×D₂₆₉	C₂³	1	2	yes	—
50	C₂³×D₂₆₉	C₂³	1	4	yes	complemented
51	C₂³×D₂₆₉	C₂³	1	8	yes	complemented
52	C₂×D₁₀₇₆	—	2	8	no	—
53	C₂×D₁₀₇₆	—	4	2	no	—
54	C₂×D₁₀₇₆	C₂³	1	8	yes	complemented
55	C₂×D₁₀₇₆	C₂³	1	4	yes	complemented
56	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
57	C₂×C₂²⋊D₂₆₉	—	2	64	no	—
58	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
59	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
60	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
61	C₂×C₂²⋊D₂₆₉	D₄	1	16	yes	complemented
62	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	—
63	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
64	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
65	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
66	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
67	D₄×D₂₆₉	—	2	64	no	—
68	C₂²×Dic₂₆₉	—	2	8	no	—
69	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
70	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
71	C₂²×Dic₂₆₉	C₂³	1	8	yes	complemented
72	C₂×C₄×D₂₆₉	—	2	8	no	—
73	C₂×C₄×D₂₆₉	C₂³	1	8	yes	complemented
74	#16864381	C₂³	1	8	yes	complemented
75	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	complemented
76	#16864379	C₂³	1	8	yes	complemented
77	#16864379	C₂³	1	8	yes	complemented
78	C₄×Dic₂₆₉	C₂³	1	4	yes	complemented
79	C₂⁴×C₂₆₉	—	2	8	no	—
80	C₂⁴×C₂₆₉	—	4	2	no	—
81	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
82	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
83	C₂⁴×C₂₆₉	C₂³	1	2	yes	—
84	C₂⁴×C₂₆₉	C₂³	1	4	yes	complemented
85	C₂×D₄×C₂₆₉	—	2	8	no	—
86	C₂×D₄×C₂₆₉	—	4	2	no	—
87	C₂×D₄×C₂₆₉	C₂³	1	8	yes	complemented
88	C₂×D₄×C₂₆₉	C₂³	1	4	yes	complemented
89	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
91	C₂²⋊C₄×C₂₆₉	C₂³	1	8	yes	complemented
92	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	complemented
93	C₂²×D₂₆₉	—	2	4	no	—
94	C₂²×D₂₆₉	—	2	4	no	—
95	C₂²×D₂₆₉	—	2	4	no	—
96	C₂²×D₂₆₉	—	2	4	no	—
97	C₂²×D₂₆₉	—	2	16	no	—
98	C₂²×D₂₆₉	—	2	4	no	—
99	C₂²×D₂₆₉	—	2	16	no	—
100	C₂²×D₂₆₉	—	2	16	no	—
101	C₂²×D₂₆₉	—	4	4	no	—
102	C₂²×D₂₆₉	—	4	8	no	—
103	C₂²×D₂₆₉	—	4	16	no	—
104	C₂²×D₂₆₉	—	4	32	no	—
105	C₂²×D₂₆₉	C₂×D₄	1	8	yes	complemented
106	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
107	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
108	D₁₀₇₆	—	2	16	no	—
109	D₁₀₇₆	—	4	4	no	—
110	C₂²⋊D₂₆₉	—	2	16	no	—
111	C₂²⋊D₂₆₉	—	2	16	no	—
112	C₂²⋊D₂₆₉	—	2	16	no	—
113	C₂²⋊D₂₆₉	—	2	16	no	—
114	C₂²⋊D₂₆₉	C₂×D₄	1	32	yes	complemented
115	C₂×Dic₂₆₉	—	2	4	no	—
116	C₂×Dic₂₆₉	—	2	16	no	—
117	C₂×Dic₂₆₉	C₂×D₄	1	8	yes	complemented
118	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
119	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
120	C₄×D₂₆₉	—	2	16	no	—
121	C₂³×C₂₆₉	—	2	4	no	—
122	C₂³×C₂₆₉	—	2	4	no	—
123	C₂³×C₂₆₉	—	2	4	no	—
124	C₂³×C₂₆₉	—	2	4	no	—
125	C₂³×C₂₆₉	—	2	16	no	—
126	C₂³×C₂₆₉	—	2	2	no	—
127	C₂³×C₂₆₉	—	2	2	no	—
128	C₂³×C₂₆₉	—	4	4	no	—
129	C₂³×C₂₆₉	—	4	16	no	—
130	C₂³×C₂₆₉	C₂×D₄	1	8	yes	complemented
131	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
132	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
133	C₂³×C₂₆₉	C₂⁴	1	4	yes	—
134	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
135	D₄×C₂₆₉	—	2	16	no	—
136	D₄×C₂₆₉	—	4	4	no	—
137	C₂×C₄×C₂₆₉	—	2	4	no	—
138	C₂×C₄×C₂₆₉	—	2	2	no	—
139	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
140	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
141	C₂²×C₂₆₉	—	2	16	no	—
142	C₂²×C₂₆₉	—	2	4	no	—
143	C₂²×C₂₆₉	—	2	4	no	—
144	C₂²×C₂₆₉	—	2	4	no	—
145	C₂²×C₂₆₉	—	2	4	no	—
146	C₂²×C₂₆₉	—	2	2	no	—
147	C₂²×C₂₆₉	—	2	2	no	—
148	C₂²×C₂₆₉	—	4	16	no	—
149	C₂²×C₂₆₉	—	4	4	no	—
150	C₂²×C₂₆₉	—	4	4	no	—
151	C₂²×C₂₆₉	C₂²×D₄	1	4	yes	—
152	C₂²×C₂₆₉	C₂²×D₄	1	8	yes	complemented
153	C₂²×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
154	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
155	C₂×D₂₆₉	—	2	16	no	—
156	C₂×D₂₆₉	—	2	4	no	—
157	C₂×D₂₆₉	—	2	4	no	—
158	C₂×D₂₆₉	—	2	4	no	—
159	C₂×D₂₆₉	—	2	4	no	—
160	C₂×D₂₆₉	—	2	4	no	—
161	C₂×D₂₆₉	—	4	16	no	—
162	C₂×D₂₆₉	—	4	32	no	—
163	C₂×D₂₆₉	—	4	8	no	—
164	C₂×D₂₆₉	C₂²×D₄	1	8	yes	complemented
165	C₄×C₂₆₉	—	2	4	no	—
166	C₄×C₂₆₉	—	2	2	no	—
167	Dic₂₆₉	—	2	4	no	—
168	Dic₂₆₉	C₂²×D₄	1	8	yes	complemented
169	C₂×C₂₆₉	—	2	8	no	—
170	C₂×C₂₆₉	—	4	2	no	—
171	C₂×C₂₆₉	—	4	2	no	—
172	C₂×C₂₆₉	D₄²	1	4	yes	complemented
173	C₂×C₂₆₉	C₂³×D₄	1	2	yes	—
174	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
175	D₂₆₉	—	2	8	no	—
176	D₂₆₉	—	4	4	no	—
177	C₂₆₉	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
178	C₂×D₄²	—	269	1	no	maximal, Sylow
179	C₂³×D₄	—	269	2	no	—
180	C₂³×D₄	—	269	2	no	—
181	D₄²	—	269	16	no	—
182	C₂×#127	—	269	1	no	—
183	C₂×#121	—	269	2	no	—
184	C₂×#121	—	269	2	no	—
185	C₂×#120	—	269	1	no	—
186	C₂×#120	—	269	2	no	—
187	C₂×#120	D₂₆₉	1	1	yes	characteristic, complemented
188	C₂×C₄×D₄	—	269	2	no	—
189	C₂⁵	—	269	1	no	—
190	C₂⁵	—	269	2	no	—
191	C₂⁵	C₂×D₂₆₉	1	1	yes	characteristic, complemented
192	C₂²×D₄	—	269	2	no	—
193	C₂²×D₄	—	269	2	no	—
194	C₂²×D₄	—	269	2	no	—
195	C₂²×D₄	—	269	2	no	—
196	C₂²×D₄	—	269	2	no	—
197	C₂²×D₄	—	269	16	no	—
198	C₂²×D₄	—	269	16	no	—
199	C₂²×D₄	—	269	2	no	—
200	C₂²×D₄	—	269	1	no	—
201	C₂²×D₄	—	538	16	no	—
202	C₂²×D₄	—	538	16	no	—
203	C₂²×D₄	C₂×D₂₆₉	1	2	yes	complemented
204	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
205	C₂³×C₄	—	269	2	no	—
206	C₂³×C₄	—	269	2	no	—
207	#127	—	269	8	no	—
208	#121	—	269	16	no	—
209	#121	—	269	16	no	—
210	#120	—	269	8	no	—
211	#120	—	269	16	no	—
212	#120	C₂×D₂₆₉	1	8	yes	complemented
213	C₄×D₄	—	269	16	no	—
214	C₂×C₄⋊C₄	—	269	2	no	—
215	C₂×C₂²⋊C₄	—	269	1	no	—
216	C₂×C₂²⋊C₄	—	269	2	no	—
217	C₂×C₂²⋊C₄	—	269	2	no	—
218	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
219	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
220	C₂×C₄²	—	269	1	no	—
221	C₂⁴	—	2	8	no	—
222	C₂⁴	—	4	2	no	—
223	C₂⁴	—	269	2	no	—
224	C₂⁴	—	269	2	no	—
225	C₂⁴	—	269	4	no	—
226	C₂⁴	—	269	8	no	—
227	C₂⁴	—	538	8	no	—
228	C₂⁴	—	538	8	no	—
229	C₂⁴	—	538	8	no	—
230	C₂⁴	—	1076	4	no	—
231	C₂⁴	—	1076	2	no	—
232	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
233	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
234	C₂⁴	C₂²×D₂₆₉	1	2	yes	—
235	C₂⁴	C₂²×D₂₆₉	1	4	yes	complemented
236	C₂×D₄	—	2	8	no	—
237	C₂×D₄	—	4	2	no	—
238	C₂×D₄	—	269	16	no	—
239	C₂×D₄	—	269	8	no	—
240	C₂×D₄	—	269	8	no	—
241	C₂×D₄	—	269	8	no	—
242	C₂×D₄	—	269	8	no	—
243	C₂×D₄	—	269	8	no	—
244	C₂×D₄	—	269	8	no	—
245	C₂×D₄	—	269	4	no	—
246	C₂×D₄	—	538	8	no	—
247	C₂×D₄	—	538	8	no	—
248	C₂×D₄	—	538	8	no	—
249	C₂×D₄	—	538	64	no	—
250	C₂×D₄	—	538	64	no	—
251	C₂×D₄	—	538	8	no	—
252	C₂×D₄	—	538	8	no	—
253	C₂×D₄	—	1076	2	no	—
254	C₂×D₄	C₂²×D₂₆₉	1	8	yes	complemented
255	C₂×D₄	C₂²×D₂₆₉	1	4	yes	complemented
256	C₂²×C₄	—	269	2	no	—
257	C₂²×C₄	—	269	8	no	—
258	C₂²×C₄	—	269	2	no	—
259	C₂²×C₄	—	269	8	no	—
260	C₂²×C₄	—	538	8	no	—
261	C₂²×C₄	—	538	8	no	—
262	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
263	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
264	C₄⋊C₄	—	269	8	no	—
265	C₂²⋊C₄	—	269	4	no	—
266	C₂²⋊C₄	—	269	8	no	—
267	C₂²⋊C₄	—	269	8	no	—
268	C₂²⋊C₄	C₂²×D₂₆₉	1	8	yes	complemented
269	C₂²⋊C₄	C₂²×D₂₆₉	1	4	yes	complemented
270	C₄²	—	269	4	no	—
271	C₂³	—	2	4	no	—
272	C₂³	—	2	4	no	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	4	no	—
275	C₂³	—	2	16	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	4	4	no	—
279	C₂³	—	4	16	no	—
280	C₂³	—	269	8	no	—
281	C₂³	—	269	4	no	—
282	C₂³	—	269	4	no	—
283	C₂³	—	538	16	no	—
284	C₂³	—	538	16	no	—
285	C₂³	—	538	4	no	—
286	C₂³	—	538	4	no	—
287	C₂³	—	538	4	no	—
288	C₂³	—	538	4	no	—
289	C₂³	—	538	16	no	—
290	C₂³	—	538	4	no	—
291	C₂³	—	1076	8	no	—
292	C₂³	—	1076	4	no	—
293	C₂³	—	1076	32	no	—
294	C₂³	—	1076	16	no	—
295	C₂³	D₄×D₂₆₉	1	8	yes	complemented
296	C₂³	C₂³×D₂₆₉	1	2	yes	—
297	C₂³	C₂³×D₂₆₉	1	2	yes	—
298	C₂³	C₂³×D₂₆₉	1	4	yes	—
299	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
300	D₄	—	2	16	no	—
301	D₄	—	4	4	no	—
302	D₄	—	269	32	no	—
303	D₄	—	538	16	no	—
304	D₄	—	538	16	no	—
305	D₄	—	538	16	no	—
306	D₄	—	538	16	no	—
307	D₄	—	538	16	no	—
308	D₄	—	1076	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	269	8	no	—
312	C₂×C₄	—	269	4	no	—
313	C₂×C₄	—	269	4	no	—
314	C₂×C₄	—	538	16	no	—
315	C₂×C₄	—	538	16	no	—
316	C₂×C₄	—	538	4	no	—
317	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
318	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	2	16	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	4	16	no	—
327	C₂²	—	4	4	no	—
328	C₂²	—	4	4	no	—
329	C₂²	—	269	8	no	—
330	C₂²	—	538	4	no	—
331	C₂²	—	538	4	no	—
332	C₂²	—	538	16	no	—
333	C₂²	—	538	4	no	—
334	C₂²	—	538	4	no	—
335	C₂²	—	538	4	no	—
336	C₂²	—	1076	32	no	—
337	C₂²	—	1076	16	no	—
338	C₂²	—	1076	8	no	—
339	C₂²	C₂×D₄×D₂₆₉	1	4	yes	—
340	C₂²	C₂×D₄×D₂₆₉	1	8	yes	complemented
341	C₂²	#22575498	1	2	yes	—
342	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
343	C₄	—	2	4	no	—
344	C₄	—	2	2	no	—
345	C₄	—	269	8	no	—
346	C₄	—	538	4	no	—
347	C₂	—	2	8	no	—
348	C₂	—	4	2	no	—
349	C₂	—	4	2	no	—
350	C₂	—	538	8	no	—
351	C₂	—	1076	4	no	—
352	C₂	#31771237	1	4	yes	direct product factor
353	C₂	C₂²×D₄×D₂₆₉	1	2	yes	—
354	C₂	C₂×#22575498	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₆₉
commutator, cosocle	C₂²×C₂₆₉	C₂⁵
Frattini	C₂²	C₂⁴×D₂₆₉
Fitting	C₂×#120×C₂₆₉	C₂
socle	C₂³×C₂₆₉	C₂⁴
hypercenter	C₂×#120	D₂₆₉
hypocenter	C₂₆₉	C₂×D₄²
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂³ ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂²⋊D₂₆₉	C₂	semidirect
2. C₂²×D₄×D₂₆₉	C₂	semidirect
3. #31771237	C₂	direct (N × H)
4. C₂×#22575449	C₂	semidirect
5. C₂×#22575426	C₂	semidirect
6. C₂×#22575425	C₂	semidirect
7. C₂×#22575423	C₂	semidirect
8. C₂×#22575421	C₂	semidirect
9. C₂×#22575413	C₂	semidirect
10. C₂×#120×C₂₆₉	C₂	semidirect
11. C₂⁴×D₂₆₉	C₂²	semidirect
12. C₂⁴×D₂₆₉	C₂²	semidirect
13. C₂²×D₁₀₇₆	C₂²	semidirect
14. C₂²×D₁₀₇₆	C₂²	semidirect
17. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
18. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
19. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
20. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
21. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
23. C₂×D₄×D₂₆₉	C₂²	semidirect
24. C₂³×Dic₂₆₉	C₂²	semidirect
25. C₂²×C₄×D₂₆₉	C₂²	semidirect
26. #22575449	C₂²	semidirect
27. #22575426	C₂²	semidirect
28. #22575425	C₂²	semidirect
29. #22575423	C₂²	semidirect
30. #22575421	C₂²	semidirect
31. #22575413	C₂²	semidirect
32. C₂×#16864381	C₂²	semidirect
33. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
34. C₂×#16864379	C₂²	semidirect
35. C₂×#16864379	C₂²	semidirect
36. C₂×C₄×Dic₂₆₉	C₂²	semidirect
37. C₂⁵×C₂₆₉	C₂²	semidirect
38. C₂²×D₄×C₂₆₉	C₂²	semidirect
39. C₂²×D₄×C₂₆₉	C₂²	semidirect
40. #120×C₂₆₉	C₂²	semidirect
41. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
42. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
50. C₂³×D₂₆₉	C₂³	semidirect
51. C₂³×D₂₆₉	C₂³	semidirect
54. C₂×D₁₀₇₆	C₂³	semidirect
55. C₂×D₁₀₇₆	C₂³	semidirect
61. C₂×C₂²⋊D₂₆₉	D₄	semidirect
63. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
64. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
65. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
66. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
71. C₂²×Dic₂₆₉	C₂³	semidirect
73. C₂×C₄×D₂₆₉	C₂³	semidirect
74. #16864381	C₂³	semidirect
75. C₂²⋊Dic₂₆₉	C₂³	semidirect
76. #16864379	C₂³	semidirect
77. #16864379	C₂³	semidirect
78. C₄×Dic₂₆₉	C₂³	semidirect
84. C₂⁴×C₂₆₉	C₂³	semidirect
87. C₂×D₄×C₂₆₉	C₂³	semidirect
88. C₂×D₄×C₂₆₉	C₂³	semidirect
91. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
92. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
105. C₂²×D₂₆₉	C₂×D₄	semidirect
114. C₂²⋊D₂₆₉	C₂×D₄	semidirect
117. C₂×Dic₂₆₉	C₂×D₄	semidirect
130. C₂³×C₂₆₉	C₂×D₄	semidirect
152. C₂²×C₂₆₉	C₂²×D₄	semidirect
164. C₂×D₂₆₉	C₂²×D₄	semidirect
168. Dic₂₆₉	C₂²×D₄	semidirect
172. C₂×C₂₆₉	D₄²	semidirect
177. C₂₆₉	C₂×D₄²	semidirect
187. C₂×#120	D₂₆₉	semidirect
191. C₂⁵	C₂×D₂₆₉	semidirect
203. C₂²×D₄	C₂×D₂₆₉	semidirect
204. C₂²×D₄	C₂×D₂₆₉	semidirect
212. #120	C₂×D₂₆₉	semidirect
218. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
219. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
235. C₂⁴	C₂²×D₂₆₉	semidirect
254. C₂×D₄	C₂²×D₂₆₉	semidirect
255. C₂×D₄	C₂²×D₂₆₉	semidirect
268. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
269. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
295. C₂³	D₄×D₂₆₉	semidirect
340. C₂²	C₂×D₄×D₂₆₉	semidirect
352. C₂	#31771237	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊D₂₆₉	2
C₂²×D₄×D₂₆₉	2
#31771237	2
C₂×#22575449	2
C₂×#22575426	2
C₂×#22575425	2
C₂×#22575423	2
C₂×#22575421	2
C₂×#22575413	2
C₂×#120×C₂₆₉	2
C₂×D₄²	269

Subgroups — C2×#31771237 #46824321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31771237 #46824321