Subgroups — C₂×#31771163 #46824184

Order 34432.

1984 conjugacy classes of subgroups.

The subgroup lattice has 340 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	#31771163	C₂	1	16	yes	maximal, direct product factor
3	C₂×#22575438	C₂	1	2	yes	maximal, complemented
4	C₂×#22575435	C₂	1	2	yes	maximal, complemented
5	C₂×#22575427	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22575425	C₂	1	2	yes	maximal, complemented
7	C₂×#22575423	C₂	1	2	yes	maximal, complemented
8	C₂×#22575421	C₂	1	2	yes	maximal, complemented
9	C₂²×#16864379	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#121×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁴×D₂₆₉	C₂²	1	1	yes	characteristic
12	C₂⁴×D₂₆₉	C₂²	1	2	yes	complemented
13	C₂²×D₁₀₇₆	C₂²	1	2	yes	—
14	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
17	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
18	C₂×D₄×D₂₆₉	—	2	16	no	—
19	C₂×D₄×D₂₆₉	C₂²	1	16	yes	complemented
20	C₂³×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	complemented
22	#22575438	C₂²	1	16	yes	complemented
23	#22575435	C₂²	1	16	yes	complemented
24	#22575427	C₂²	1	8	yes	complemented
25	#22575425	C₂²	1	16	yes	complemented
26	#22575423	C₂²	1	16	yes	complemented
27	#22575421	C₂²	1	16	yes	complemented
28	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#16864381	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Dic₂₆₉	C₂²	1	2	yes	complemented
31	C₂×#16864379	C₂²	1	2	yes	complemented
32	C₂×#16864379	C₂²	1	2	yes	complemented
33	C₂×#16864379	C₂²	1	2	yes	complemented
34	C₂×#16864379	C₂²	1	2	yes	complemented
35	C₂×#16864379	C₂²	1	8	yes	complemented
36	C₂²×D₄×C₂₆₉	C₂²	1	2	yes	complemented
37	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
39	#121×C₂₆₉	C₂²	1	8	yes	complemented
40	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
42	C₂³×D₂₆₉	—	2	8	no	—
43	C₂³×D₂₆₉	—	4	2	no	—
44	C₂³×D₂₆₉	—	4	2	no	—
45	C₂³×D₂₆₉	—	4	4	no	—
46	C₂³×D₂₆₉	—	4	4	no	—
47	C₂³×D₂₆₉	D₄	1	8	yes	complemented
48	C₂³×D₂₆₉	C₂³	1	2	yes	—
49	C₂³×D₂₆₉	C₂³	1	2	yes	—
50	C₂³×D₂₆₉	C₂³	1	4	yes	—
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	—
55	C₂×D₁₀₇₆	C₂³	1	4	yes	complemented
56	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
57	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
58	C₂×C₂²⋊D₂₆₉	—	4	4	no	—
59	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	—
60	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
61	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
62	D₄×D₂₆₉	—	2	64	no	—
63	C₂²×Dic₂₆₉	—	4	2	no	—
64	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
65	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
66	C₂²×Dic₂₆₉	C₂³	1	4	yes	complemented
67	C₂×C₄×D₂₆₉	—	2	8	no	—
68	C₂×C₄×D₂₆₉	C₂³	1	8	yes	complemented
69	C₄⋊Dic₂₆₉	C₂³	1	4	yes	complemented
70	#16864381	C₂³	1	8	yes	complemented
71	C₂²⋊Dic₂₆₉	C₂³	1	8	yes	complemented
72	#16864379	C₂³	1	8	yes	complemented
73	#16864379	C₂³	1	8	yes	complemented
74	#16864379	C₂³	1	8	yes	complemented
75	#16864379	C₂³	1	8	yes	complemented
76	C₂⁴×C₂₆₉	C₂³	1	2	yes	—
77	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
78	C₂×D₄×C₂₆₉	—	2	8	no	—
79	C₂×D₄×C₂₆₉	—	4	2	no	—
80	C₂×D₄×C₂₆₉	C₂³	1	8	yes	complemented
81	C₂×D₄×C₂₆₉	C₂³	1	4	yes	complemented
82	C₂²×C₄×C₂₆₉	—	4	2	no	—
83	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
86	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	complemented
87	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	complemented
88	C₂²⋊C₄×C₂₆₉	C₂³	1	8	yes	complemented
89	C₂²×D₂₆₉	—	2	4	no	—
90	C₂²×D₂₆₉	—	2	4	no	—
91	C₂²×D₂₆₉	—	2	4	no	—
92	C₂²×D₂₆₉	—	2	4	no	—
93	C₂²×D₂₆₉	—	2	4	no	—
94	C₂²×D₂₆₉	—	2	16	no	—
95	C₂²×D₂₆₉	—	4	16	no	—
96	C₂²×D₂₆₉	—	4	4	no	—
97	C₂²×D₂₆₉	—	4	4	no	—
98	C₂²×D₂₆₉	—	4	8	no	—
99	C₂²×D₂₆₉	—	4	8	no	—
100	C₂²×D₂₆₉	—	4	32	no	—
101	C₂²×D₂₆₉	C₂×D₄	1	8	yes	—
102	C₂²×D₂₆₉	C₂×D₄	1	16	yes	complemented
103	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
104	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
105	D₁₀₇₆	—	2	16	no	—
106	D₁₀₇₆	—	4	4	no	—
107	C₂²⋊D₂₆₉	—	2	16	no	—
108	C₂²⋊D₂₆₉	—	2	16	no	—
109	C₂²⋊D₂₆₉	—	4	8	no	—
110	C₂×Dic₂₆₉	—	2	4	no	—
111	C₂×Dic₂₆₉	—	2	4	no	—
112	C₂×Dic₂₆₉	—	4	4	no	—
113	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
114	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
115	C₄×D₂₆₉	—	2	16	no	—
116	C₂³×C₂₆₉	—	2	2	no	—
117	C₂³×C₂₆₉	—	2	2	no	—
118	C₂³×C₂₆₉	—	2	4	no	—
119	C₂³×C₂₆₉	—	2	4	no	—
120	C₂³×C₂₆₉	—	2	4	no	—
121	C₂³×C₂₆₉	C₂×D₄	1	4	yes	—
122	C₂³×C₂₆₉	C₂⁴	1	4	yes	—
123	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
124	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
125	D₄×C₂₆₉	—	2	16	no	—
126	D₄×C₂₆₉	—	4	4	no	—
127	C₂×C₄×C₂₆₉	—	2	4	no	—
128	C₂×C₄×C₂₆₉	—	2	2	no	—
129	C₂×C₄×C₂₆₉	—	2	2	no	—
130	C₂×C₄×C₂₆₉	—	4	4	no	—
131	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
132	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
133	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
134	C₂²×C₂₆₉	—	2	8	no	—
135	C₂²×C₂₆₉	—	2	2	no	—
136	C₂²×C₂₆₉	—	2	2	no	—
137	C₂²×C₂₆₉	—	2	4	no	—
138	C₂²×C₂₆₉	—	2	4	no	—
139	C₂²×C₂₆₉	—	2	4	no	—
140	C₂²×C₂₆₉	—	4	8	no	—
141	C₂²×C₂₆₉	C₂²×D₄	1	4	yes	—
142	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
143	C₂²×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
144	C₂²×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
145	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
146	C₂×D₂₆₉	—	2	16	no	—
147	C₂×D₂₆₉	—	2	4	no	—
148	C₂×D₂₆₉	—	2	4	no	—
149	C₂×D₂₆₉	—	2	4	no	—
150	C₂×D₂₆₉	—	2	4	no	—
151	C₂×D₂₆₉	—	2	4	no	—
152	C₂×D₂₆₉	—	4	16	no	—
153	C₂×D₂₆₉	—	4	32	no	—
154	C₂×D₂₆₉	—	4	8	no	—
155	C₂×D₂₆₉	C₂²×D₄	1	8	yes	—
156	C₄×C₂₆₉	—	2	4	no	—
157	C₄×C₂₆₉	—	2	2	no	—
158	C₄×C₂₆₉	—	2	2	no	—
159	Dic₂₆₉	—	2	4	no	—
160	Dic₂₆₉	—	2	4	no	—
161	C₂×C₂₆₉	—	2	4	no	—
162	C₂×C₂₆₉	—	4	4	no	—
163	C₂×C₂₆₉	#534	1	4	yes	complemented
164	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
165	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
167	D₂₆₉	—	2	8	no	—
168	D₂₆₉	—	4	4	no	—
169	C₂₆₉	C₂×#534	1	1	yes	characteristic, complemented, Sylow
170	C₂×#534	—	269	1	no	maximal, Sylow
171	C₂³×D₄	—	269	2	no	—
172	#534	—	269	16	no	—
173	C₂×#123	—	269	2	no	—
174	C₂×#123	—	269	2	no	—
175	C₂×#121	—	269	2	no	—
176	C₂×#121	—	269	1	no	—
177	C₂×#121	D₂₆₉	1	1	yes	characteristic, complemented
178	C₂×#120	—	269	2	no	—
179	C₂×#120	—	269	2	no	—
180	C₂²×C₂²⋊C₄	—	269	1	no	—
181	C₂⁵	—	269	1	no	—
182	C₂⁵	—	269	2	no	—
183	C₂²×D₄	—	269	2	no	—
184	C₂²×D₄	—	269	2	no	—
185	C₂²×D₄	—	269	2	no	—
186	C₂²×D₄	—	269	16	no	—
187	C₂²×D₄	—	269	2	no	—
188	C₂²×D₄	—	269	1	no	—
189	C₂²×D₄	—	538	16	no	—
190	C₂²×D₄	C₂×D₂₆₉	1	2	yes	complemented
191	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
192	C₂³×C₄	—	269	1	no	—
193	C₂³×C₄	—	269	2	no	—
194	C₂³×C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
195	#123	—	269	16	no	—
196	#123	—	269	16	no	—
197	#121	—	269	16	no	—
198	#121	—	269	8	no	—
199	#121	C₂×D₂₆₉	1	8	yes	complemented
200	#120	—	269	16	no	—
201	#120	—	269	16	no	—
202	C₂×C₄⋊C₄	—	269	2	no	—
203	C₂×C₄⋊C₄	—	269	1	no	—
204	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
205	C₂×C₂²⋊C₄	—	269	2	no	—
206	C₂×C₂²⋊C₄	—	269	2	no	—
207	C₂×C₂²⋊C₄	—	269	2	no	—
208	C₂×C₂²⋊C₄	—	269	2	no	—
209	C₂×C₂²⋊C₄	—	269	2	no	—
210	C₂×C₂²⋊C₄	—	269	8	no	—
211	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
212	C₂⁴	—	269	2	no	—
213	C₂⁴	—	269	8	no	—
214	C₂⁴	—	269	4	no	—
215	C₂⁴	—	269	2	no	—
216	C₂⁴	—	269	8	no	—
217	C₂⁴	—	538	8	no	—
218	C₂⁴	—	1076	2	no	—
219	C₂⁴	—	1076	2	no	—
220	C₂⁴	—	1076	4	no	—
221	C₂⁴	—	1076	4	no	—
222	C₂⁴	C₂²×D₂₆₉	1	2	yes	—
223	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
224	C₂×D₄	—	2	8	no	—
225	C₂×D₄	—	4	2	no	—
226	C₂×D₄	—	269	8	no	—
227	C₂×D₄	—	269	8	no	—
228	C₂×D₄	—	269	8	no	—
229	C₂×D₄	—	269	8	no	—
230	C₂×D₄	—	269	4	no	—
231	C₂×D₄	—	538	8	no	—
232	C₂×D₄	—	538	64	no	—
233	C₂×D₄	—	538	8	no	—
234	C₂×D₄	—	538	8	no	—
235	C₂×D₄	—	1076	2	no	—
236	C₂×D₄	—	1076	4	no	—
237	C₂×D₄	C₂²×D₂₆₉	1	8	yes	complemented
238	C₂×D₄	C₂²×D₂₆₉	1	4	yes	complemented
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	269	2	no	—
241	C₂²×C₄	—	269	2	no	—
242	C₂²×C₄	—	269	4	no	—
243	C₂²×C₄	—	269	8	no	—
244	C₂²×C₄	—	538	8	no	—
245	C₂²×C₄	—	1076	2	no	—
246	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
247	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
248	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
249	C₂²×C₄	C₂²×D₂₆₉	1	4	yes	complemented
250	C₄⋊C₄	—	269	8	no	—
251	C₄⋊C₄	—	269	4	no	—
252	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	complemented
253	C₂²⋊C₄	—	269	8	no	—
254	C₂²⋊C₄	—	269	8	no	—
255	C₂²⋊C₄	—	269	8	no	—
256	C₂²⋊C₄	—	269	8	no	—
257	C₂²⋊C₄	—	269	8	no	—
258	C₂²⋊C₄	C₂²×D₂₆₉	1	8	yes	complemented
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	2	4	no	—
262	C₂³	—	2	4	no	—
263	C₂³	—	2	4	no	—
264	C₂³	—	269	8	no	—
265	C₂³	—	269	4	no	—
266	C₂³	—	269	16	no	—
267	C₂³	—	269	4	no	—
268	C₂³	—	538	16	no	—
269	C₂³	—	538	4	no	—
270	C₂³	—	538	4	no	—
271	C₂³	—	538	4	no	—
272	C₂³	—	538	4	no	—
273	C₂³	—	538	4	no	—
274	C₂³	—	1076	16	no	—
275	C₂³	—	1076	4	no	—
276	C₂³	—	1076	4	no	—
277	C₂³	—	1076	8	no	—
278	C₂³	—	1076	8	no	—
279	C₂³	—	1076	32	no	—
280	C₂³	D₄×D₂₆₉	1	4	yes	—
281	C₂³	C₂³×D₂₆₉	1	4	yes	—
282	C₂³	C₂³×D₂₆₉	1	2	yes	—
283	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
284	D₄	—	2	16	no	—
285	D₄	—	4	4	no	—
286	D₄	—	538	16	no	—
287	D₄	—	538	16	no	—
288	D₄	—	538	16	no	—
289	D₄	—	1076	4	no	—
290	D₄	—	1076	8	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	269	4	no	—
296	C₂×C₄	—	269	4	no	—
297	C₂×C₄	—	538	16	no	—
298	C₂×C₄	—	538	4	no	—
299	C₂×C₄	—	538	4	no	—
300	C₂×C₄	—	1076	4	no	—
301	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
302	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
303	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
304	C₂²	—	2	8	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	4	no	—
309	C₂²	—	2	4	no	—
310	C₂²	—	4	8	no	—
311	C₂²	—	269	8	no	—
312	C₂²	—	538	16	no	—
313	C₂²	—	538	4	no	—
314	C₂²	—	538	4	no	—
315	C₂²	—	538	4	no	—
316	C₂²	—	538	4	no	—
317	C₂²	—	538	4	no	—
318	C₂²	—	1076	16	no	—
319	C₂²	—	1076	32	no	—
320	C₂²	—	1076	8	no	—
321	C₂²	C₂×D₄×D₂₆₉	1	4	yes	—
322	C₂²	C₂×D₄×D₂₆₉	1	2	yes	—
323	C₂²	#22575498	1	2	yes	—
324	C₂²	#22575499	1	2	yes	—
325	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	538	4	no	—
330	C₄	—	538	4	no	—
331	C₂	—	2	4	no	—
332	C₂	—	4	4	no	—
333	C₂	—	538	8	no	—
334	C₂	—	1076	4	no	—
335	C₂	#31771163	1	4	yes	direct product factor
336	C₂	C₂²×D₄×D₂₆₉	1	1	yes	characteristic
337	C₂	C₂×#22575498	1	1	yes	characteristic
338	C₂	C₂×#22575499	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	C₂×#534
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. #31771163	C₂	direct (N × H)
3. C₂×#22575438	C₂	semidirect
4. C₂×#22575435	C₂	semidirect
5. C₂×#22575427	C₂	semidirect
6. C₂×#22575425	C₂	semidirect
7. C₂×#22575423	C₂	semidirect
8. C₂×#22575421	C₂	semidirect
9. C₂²×#16864379	C₂	semidirect
10. C₂×#121×C₂₆₉	C₂	semidirect
12. C₂⁴×D₂₆₉	C₂²	semidirect
14. C₂²×D₁₀₇₆	C₂²	semidirect
16. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
17. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
19. C₂×D₄×D₂₆₉	C₂²	semidirect
20. C₂³×Dic₂₆₉	C₂²	semidirect
21. C₂²×C₄×D₂₆₉	C₂²	semidirect
22. #22575438	C₂²	semidirect
23. #22575435	C₂²	semidirect
24. #22575427	C₂²	semidirect
25. #22575425	C₂²	semidirect
26. #22575423	C₂²	semidirect
27. #22575421	C₂²	semidirect
28. C₂×C₄⋊Dic₂₆₉	C₂²	semidirect
29. C₂×#16864381	C₂²	semidirect
30. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
31. C₂×#16864379	C₂²	semidirect
32. C₂×#16864379	C₂²	semidirect
33. C₂×#16864379	C₂²	semidirect
34. C₂×#16864379	C₂²	semidirect
35. C₂×#16864379	C₂²	semidirect
36. C₂²×D₄×C₂₆₉	C₂²	semidirect
37. C₂²×D₄×C₂₆₉	C₂²	semidirect
38. C₂³×C₄×C₂₆₉	C₂²	semidirect
39. #121×C₂₆₉	C₂²	semidirect
40. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
41. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
47. C₂³×D₂₆₉	D₄	semidirect
51. C₂³×D₂₆₉	C₂³	semidirect
55. C₂×D₁₀₇₆	C₂³	semidirect
60. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
61. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
66. C₂²×Dic₂₆₉	C₂³	semidirect
68. C₂×C₄×D₂₆₉	C₂³	semidirect
69. C₄⋊Dic₂₆₉	C₂³	semidirect
70. #16864381	C₂³	semidirect
71. C₂²⋊Dic₂₆₉	C₂³	semidirect
72. #16864379	C₂³	semidirect
73. #16864379	C₂³	semidirect
74. #16864379	C₂³	semidirect
75. #16864379	C₂³	semidirect
80. C₂×D₄×C₂₆₉	C₂³	semidirect
81. C₂×D₄×C₂₆₉	C₂³	semidirect
86. C₂²×C₄×C₂₆₉	C₂³	semidirect
87. C₄⋊C₄×C₂₆₉	C₂³	semidirect
88. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
102. C₂²×D₂₆₉	C₂×D₄	semidirect
163. C₂×C₂₆₉	#534	semidirect
169. C₂₆₉	C₂×#534	semidirect
177. C₂×#121	D₂₆₉	semidirect
190. C₂²×D₄	C₂×D₂₆₉	semidirect
191. C₂²×D₄	C₂×D₂₆₉	semidirect
194. C₂³×C₄	C₂×D₂₆₉	semidirect
199. #121	C₂×D₂₆₉	semidirect
204. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
211. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
237. C₂×D₄	C₂²×D₂₆₉	semidirect
238. C₂×D₄	C₂²×D₂₆₉	semidirect
249. C₂²×C₄	C₂²×D₂₆₉	semidirect
252. C₄⋊C₄	C₂²×D₂₆₉	semidirect
258. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
335. C₂	#31771163	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
#31771163	2
C₂×#22575438	2
C₂×#22575435	2
C₂×#22575427	2
C₂×#22575425	2
C₂×#22575423	2
C₂×#22575421	2
C₂²×#16864379	2
C₂×#121×C₂₆₉	2
C₂×#534	269

Subgroups — C2×#31771163 #46824184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31771163 #46824184