Subgroups — C₂×#31771252 #46824337

Order 34432.

1900 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16864402	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771252	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22575440	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22575435	C₂	1	2	yes	maximal, complemented
6	C₂×#22575433	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22575424	C₂	1	2	yes	maximal, complemented
8	C₂×#22575421	C₂	1	2	yes	maximal, complemented
9	C₂×#22575415	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₂²⋊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	C₂×#16864402	—	2	8	no	—
15	C₂×#16864402	C₂²	1	8	yes	complemented
16	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
21	C₂×D₄×D₂₆₉	—	2	8	no	—
22	C₂×D₄×D₂₆₉	C₂²	1	8	yes	complemented
23	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	complemented
25	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	complemented
26	#22575440	C₂²	1	8	yes	complemented
27	#22575435	C₂²	1	16	yes	complemented
28	#22575433	C₂²	1	8	yes	complemented
29	#22575424	C₂²	1	16	yes	complemented
30	#22575421	C₂²	1	16	yes	complemented
31	#22575415	C₂²	1	8	yes	complemented
32	C₄×C₂²⋊D₂₆₉	C₂²	1	8	yes	complemented
33	C₂×C₄⋊Dic₂₆₉	C₂²	1	2	yes	complemented
34	C₂×#16864381	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊Dic₂₆₉	C₂²	1	2	yes	complemented
36	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊Dic₂₆₉	C₂²	1	2	yes	complemented
38	C₂×#16864379	C₂²	1	1	yes	characteristic
39	C₂×#16864379	C₂²	1	2	yes	—
40	C₂×#16864379	C₂²	1	2	yes	complemented
41	C₂²⋊C₄×D₂₆₉	C₂²	1	16	yes	complemented
42	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
43	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
44	C₂²×D₄×C₂₆₉	C₂²	1	2	yes	complemented
45	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
46	#121×C₂₆₉	C₂²	1	8	yes	complemented
47	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
49	C₂³×D₂₆₉	—	2	8	no	—
50	C₂³×D₂₆₉	—	2	8	no	—
51	C₂³×D₂₆₉	—	4	4	no	—
52	C₂³×D₂₆₉	C₂³	1	8	yes	—
53	C₂³×D₂₆₉	C₂³	1	2	yes	—
54	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
55	#16864402	—	2	32	no	—
56	C₂×Dic₅₃₈	—	2	4	no	—
57	C₂×Dic₅₃₈	C₂³	1	4	yes	complemented
58	C₂×D₁₀₇₆	D₄	1	8	yes	complemented
59	C₂×D₁₀₇₆	C₂³	1	4	yes	—
60	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
61	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
62	C₂×C₂²⋊D₂₆₉	—	2	4	no	—
63	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
64	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	—
65	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	complemented
66	D₄×D₂₆₉	—	2	32	no	—
67	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
68	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
69	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
70	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
71	C₂×C₄×D₂₆₉	—	2	8	no	—
72	C₂×C₄×D₂₆₉	—	2	4	no	—
73	C₂×C₄×D₂₆₉	—	4	4	no	—
74	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
75	C₂×C₄×D₂₆₉	C₂³	1	8	yes	complemented
76	C₂×C₄×D₂₆₉	C₂³	1	8	yes	complemented
77	C₄⋊Dic₂₆₉	C₂³	1	8	yes	complemented
78	#16864381	C₂³	1	4	yes	complemented
79	C₂²⋊Dic₂₆₉	C₂³	1	8	yes	complemented
80	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	complemented
81	C₂²⋊Dic₂₆₉	C₂³	1	8	yes	complemented
82	#16864379	C₂³	1	4	yes	—
83	#16864379	C₂³	1	8	yes	—
84	#16864379	C₂³	1	8	yes	complemented
85	C₄×Dic₂₆₉	C₂³	1	4	yes	complemented
86	C₂⁴×C₂₆₉	C₂³	1	2	yes	—
87	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
88	C₂×D₄×C₂₆₉	—	2	4	no	—
89	C₂×D₄×C₂₆₉	—	4	4	no	—
90	C₂×D₄×C₂₆₉	C₂³	1	4	yes	—
91	C₂×D₄×C₂₆₉	C₂³	1	8	yes	complemented
92	C₂²×C₄×C₂₆₉	—	2	4	no	—
93	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
94	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	complemented
97	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	complemented
98	C₂²⋊C₄×C₂₆₉	C₂³	1	8	yes	complemented
99	C₂²×D₂₆₉	—	2	2	no	—
100	C₂²×D₂₆₉	—	2	4	no	—
101	C₂²×D₂₆₉	—	2	4	no	—
102	C₂²×D₂₆₉	—	2	2	no	—
103	C₂²×D₂₆₉	—	2	16	no	—
104	C₂²×D₂₆₉	—	2	16	no	—
105	C₂²×D₂₆₉	—	4	8	no	—
106	C₂²×D₂₆₉	—	4	32	no	—
107	C₂²×D₂₆₉	C₂×D₄	1	8	yes	—
108	C₂²×D₂₆₉	#41	1	4	yes	complemented
109	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
110	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
111	Dic₅₃₈	—	2	8	no	—
112	D₁₀₇₆	C₂×D₄	1	16	yes	complemented
113	C₂²⋊D₂₆₉	—	2	16	no	—
114	C₂²⋊D₂₆₉	—	2	16	no	—
115	C₂²⋊D₂₆₉	—	2	8	no	—
116	C₂×Dic₂₆₉	—	2	2	no	—
117	C₂×Dic₂₆₉	—	2	4	no	—
118	C₂×Dic₂₆₉	—	2	2	no	—
119	C₂×Dic₂₆₉	—	2	2	no	—
120	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
121	C₂×Dic₂₆₉	C₂⁴	1	2	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	8	no	—
126	C₄×D₂₆₉	—	4	8	no	—
127	C₂³×C₂₆₉	—	2	2	no	—
128	C₂³×C₂₆₉	—	2	4	no	—
129	C₂³×C₂₆₉	—	2	2	no	—
130	C₂³×C₂₆₉	—	2	4	no	—
131	C₂³×C₂₆₉	—	2	2	no	—
132	C₂³×C₂₆₉	—	2	4	no	—
133	C₂³×C₂₆₉	C₂⁴	1	4	yes	—
134	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
135	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
136	D₄×C₂₆₉	—	2	8	no	—
137	D₄×C₂₆₉	—	4	8	no	—
138	C₂×C₄×C₂₆₉	—	2	2	no	—
139	C₂×C₄×C₂₆₉	—	2	4	no	—
140	C₂×C₄×C₂₆₉	—	2	8	no	—
141	C₂×C₄×C₂₆₉	C₂×D₄	1	4	yes	—
142	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
143	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
144	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
145	C₂²×C₂₆₉	—	2	2	no	—
146	C₂²×C₂₆₉	—	2	4	no	—
147	C₂²×C₂₆₉	—	2	2	no	—
148	C₂²×C₂₆₉	—	2	4	no	—
149	C₂²×C₂₆₉	—	2	2	no	—
150	C₂²×C₂₆₉	—	2	4	no	—
151	C₂²×C₂₆₉	—	4	4	no	—
152	C₂²×C₂₆₉	—	4	8	no	—
153	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
154	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
155	C₂²×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
156	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
157	C₂×D₂₆₉	—	2	8	no	—
158	C₂×D₂₆₉	—	2	16	no	—
159	C₂×D₂₆₉	—	2	2	no	—
160	C₂×D₂₆₉	—	2	4	no	—
161	C₂×D₂₆₉	—	2	4	no	—
162	C₂×D₂₆₉	—	2	2	no	—
163	C₂×D₂₆₉	—	4	32	no	—
164	C₂×D₂₆₉	C₂²×D₄	1	8	yes	—
165	C₂×D₂₆₉	C₂×#41	1	4	yes	complemented
166	C₄×C₂₆₉	—	2	2	no	—
167	C₄×C₂₆₉	—	2	4	no	—
168	C₄×C₂₆₉	C₂²×D₄	1	4	yes	—
169	Dic₂₆₉	—	2	2	no	—
170	Dic₂₆₉	—	2	4	no	—
171	Dic₂₆₉	—	2	2	no	—
172	Dic₂₆₉	—	2	2	no	—
173	C₂×C₂₆₉	—	4	4	no	—
174	C₂×C₂₆₉	—	4	2	no	—
175	C₂×C₂₆₉	#546	1	4	yes	complemented
176	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
177	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
178	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
179	D₂₆₉	—	2	4	no	—
180	D₂₆₉	—	2	8	no	—
181	C₂₆₉	C₂×#546	1	1	yes	characteristic, complemented, Sylow
182	C₂×#546	—	269	1	no	maximal, Sylow
183	C₂²×#41	—	269	1	no	—
184	C₂³×D₄	—	269	1	no	—
185	#546	—	269	16	no	—
186	C₂×#124	—	269	1	no	—
187	C₂×#123	—	269	2	no	—
188	C₂×C₂²⋊Q₈	—	269	1	no	—
189	C₂×#121	—	269	2	no	—
190	C₂×#121	D₂₆₉	1	1	yes	characteristic, complemented
191	C₂×#120	—	269	2	no	—
192	C₂×C₄×D₄	—	269	1	no	—
193	C₂×C₄×D₄	—	269	1	no	—
194	C₂²×C₂²⋊C₄	—	269	2	no	—
195	C₂⁵	—	269	2	no	—
196	C₂×#41	—	269	8	no	—
197	C₂×#41	—	538	8	no	—
198	C₂²×Q₈	—	269	1	no	—
199	C₂²×D₄	—	269	1	no	—
200	C₂²×D₄	—	269	2	no	—
201	C₂²×D₄	—	269	2	no	—
202	C₂²×D₄	—	269	8	no	—
203	C₂²×D₄	—	269	1	no	—
204	C₂²×D₄	—	538	8	no	—
205	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic
206	C₂²×D₄	C₂×D₂₆₉	1	2	yes	complemented
207	C₂³×C₄	—	269	2	no	—
208	C₂³×C₄	—	269	1	no	—
209	C₂³×C₄	—	269	2	no	—
210	C₂³×C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
211	#124	—	269	8	no	—
212	#123	—	269	16	no	—
213	C₂²⋊Q₈	—	269	8	no	—
214	#121	—	269	16	no	—
215	#121	C₂×D₂₆₉	1	8	yes	complemented
216	#120	—	269	16	no	—
217	C₄×D₄	—	269	8	no	—
218	C₄×D₄	—	269	8	no	—
219	C₂×C₄⋊C₄	—	269	1	no	—
220	C₂×C₄⋊C₄	—	269	2	no	—
221	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
222	C₂×C₂²⋊C₄	—	269	2	no	—
223	C₂×C₂²⋊C₄	—	269	1	no	—
224	C₂×C₂²⋊C₄	—	269	2	no	—
225	C₂×C₂²⋊C₄	—	269	1	no	—
226	C₂×C₂²⋊C₄	—	269	2	no	—
227	C₂×C₂²⋊C₄	—	269	2	no	—
228	C₂×C₂²⋊C₄	—	269	16	no	—
229	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
230	C₂×C₄²	—	269	1	no	—
231	C₂⁴	—	269	1	no	—
232	C₂⁴	—	269	2	no	—
233	C₂⁴	—	269	8	no	—
234	C₂⁴	—	538	8	no	—
235	C₂⁴	—	538	8	no	—
236	C₂⁴	—	1076	4	no	—
237	C₂⁴	C₂²×D₂₆₉	1	2	yes	—
238	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
239	#41	—	538	32	no	—
240	C₂×Q₈	—	269	4	no	—
241	C₂×Q₈	—	538	4	no	—
242	C₂×D₄	—	2	4	no	—
243	C₂×D₄	—	4	4	no	—
244	C₂×D₄	—	269	4	no	—
245	C₂×D₄	—	269	8	no	—
246	C₂×D₄	—	269	8	no	—
247	C₂×D₄	—	269	8	no	—
248	C₂×D₄	—	269	4	no	—
249	C₂×D₄	—	538	32	no	—
250	C₂×D₄	—	538	8	no	—
251	C₂×D₄	—	538	8	no	—
252	C₂×D₄	—	538	4	no	—
253	C₂×D₄	C₂²×D₂₆₉	1	4	yes	—
254	C₂×D₄	C₂²×D₂₆₉	1	8	yes	complemented
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	269	1	no	—
257	C₂²×C₄	—	269	1	no	—
258	C₂²×C₄	—	269	2	no	—
259	C₂²×C₄	—	269	1	no	—
260	C₂²×C₄	—	269	8	no	—
261	C₂²×C₄	—	269	4	no	—
262	C₂²×C₄	—	269	8	no	—
263	C₂²×C₄	—	538	8	no	—
264	C₂²×C₄	—	538	4	no	—
265	C₂²×C₄	—	1076	4	no	—
266	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
267	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₂₆₉	1	4	yes	complemented
270	C₄⋊C₄	—	269	4	no	—
271	C₄⋊C₄	—	269	8	no	—
272	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	complemented
273	C₂²⋊C₄	—	269	8	no	—
274	C₂²⋊C₄	—	269	4	no	—
275	C₂²⋊C₄	—	269	8	no	—
276	C₂²⋊C₄	—	269	4	no	—
277	C₂²⋊C₄	—	269	8	no	—
278	C₂²⋊C₄	—	269	8	no	—
279	C₂²⋊C₄	C₂²×D₂₆₉	1	8	yes	complemented
280	C₄²	—	269	4	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	4	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	4	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	269	8	no	—
288	C₂³	—	269	4	no	—
289	C₂³	—	269	2	no	—
290	C₂³	—	269	4	no	—
291	C₂³	—	538	16	no	—
292	C₂³	—	538	16	no	—
293	C₂³	—	538	2	no	—
294	C₂³	—	538	4	no	—
295	C₂³	—	538	4	no	—
296	C₂³	—	538	2	no	—
297	C₂³	—	1076	8	no	—
298	C₂³	—	1076	32	no	—
299	C₂³	C₂³×D₂₆₉	1	4	yes	—
300	C₂³	C₂³×D₂₆₉	1	2	yes	—
301	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
302	Q₈	—	538	8	no	—
303	D₄	—	2	8	no	—
304	D₄	—	4	8	no	—
305	D₄	—	269	16	no	—
306	D₄	—	538	16	no	—
307	D₄	—	538	16	no	—
308	D₄	—	538	8	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	269	2	no	—
313	C₂×C₄	—	269	2	no	—
314	C₂×C₄	—	269	4	no	—
315	C₂×C₄	—	269	2	no	—
316	C₂×C₄	—	538	16	no	—
317	C₂×C₄	—	538	2	no	—
318	C₂×C₄	—	538	4	no	—
319	C₂×C₄	—	538	2	no	—
320	C₂×C₄	—	538	2	no	—
321	C₂×C₄	—	538	8	no	—
322	C₂×C₄	—	1076	8	no	—
323	C₂×C₄	D₄×D₂₆₉	1	4	yes	—
324	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
325	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
326	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	4	8	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	269	8	no	—
336	C₂²	—	269	4	no	—
337	C₂²	—	538	2	no	—
338	C₂²	—	538	4	no	—
339	C₂²	—	538	4	no	—
340	C₂²	—	538	2	no	—
341	C₂²	—	538	8	no	—
342	C₂²	—	538	16	no	—
343	C₂²	—	1076	32	no	—
344	C₂²	C₂×D₄×D₂₆₉	1	2	yes	—
345	C₂²	#41×D₂₆₉	1	2	yes	—
346	C₂²	#22575498	1	2	yes	—
347	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	4	no	—
350	C₄	—	538	2	no	—
351	C₄	—	538	4	no	—
352	C₄	—	538	2	no	—
353	C₄	—	538	2	no	—
354	C₄	C₂×D₄×D₂₆₉	1	4	yes	—
355	C₂	—	4	4	no	—
356	C₂	—	4	2	no	—
357	C₂	—	538	4	no	—
358	C₂	—	538	8	no	—
359	C₂	#31771252	1	4	yes	direct product factor
360	C₂	C₂²×D₄×D₂₆₉	1	1	yes	characteristic
361	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
362	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×#121×C₂₆₉	C₂
socle	C₂³×C₂₆₉	C₂⁴
hypercenter	C₂×#121	D₂₆₉
hypocenter	C₂₆₉	C₂×#546
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×#16864402	C₂	semidirect
2. C₂²×D₄×D₂₆₉	C₂	semidirect
3. #31771252	C₂	direct (N × H)
4. C₂×#22575440	C₂	semidirect
5. C₂×#22575435	C₂	semidirect
6. C₂×#22575433	C₂	semidirect
7. C₂×#22575424	C₂	semidirect
8. C₂×#22575421	C₂	semidirect
9. C₂×#22575415	C₂	semidirect
10. C₂×C₄×C₂²⋊D₂₆₉	C₂	semidirect
11. C₂×C₂²⋊C₄×D₂₆₉	C₂	semidirect
12. C₂×#121×C₂₆₉	C₂	semidirect
15. C₂×#16864402	C₂²	semidirect
16. C₂²×Dic₅₃₈	C₂²	semidirect
20. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
22. C₂×D₄×D₂₆₉	C₂²	semidirect
24. C₂²×C₄×D₂₆₉	C₂²	semidirect
25. C₂²×C₄×D₂₆₉	C₂²	semidirect
26. #22575440	C₂²	semidirect
27. #22575435	C₂²	semidirect
28. #22575433	C₂²	semidirect
29. #22575424	C₂²	semidirect
30. #22575421	C₂²	semidirect
31. #22575415	C₂²	semidirect
32. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
33. C₂×C₄⋊Dic₂₆₉	C₂²	semidirect
34. C₂×#16864381	C₂²	semidirect
35. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
36. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
37. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
40. C₂×#16864379	C₂²	semidirect
41. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
42. C₂×C₄×Dic₂₆₉	C₂²	semidirect
44. C₂²×D₄×C₂₆₉	C₂²	semidirect
45. C₂³×C₄×C₂₆₉	C₂²	semidirect
46. #121×C₂₆₉	C₂²	semidirect
47. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
57. C₂×Dic₅₃₈	C₂³	semidirect
58. C₂×D₁₀₇₆	D₄	semidirect
65. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
75. C₂×C₄×D₂₆₉	C₂³	semidirect
76. C₂×C₄×D₂₆₉	C₂³	semidirect
77. C₄⋊Dic₂₆₉	C₂³	semidirect
78. #16864381	C₂³	semidirect
79. C₂²⋊Dic₂₆₉	C₂³	semidirect
80. C₂²⋊Dic₂₆₉	C₂³	semidirect
81. C₂²⋊Dic₂₆₉	C₂³	semidirect
84. #16864379	C₂³	semidirect
85. C₄×Dic₂₆₉	C₂³	semidirect
91. C₂×D₄×C₂₆₉	C₂³	semidirect
96. C₂²×C₄×C₂₆₉	C₂³	semidirect
97. C₄⋊C₄×C₂₆₉	C₂³	semidirect
98. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
108. C₂²×D₂₆₉	#41	semidirect
112. D₁₀₇₆	C₂×D₄	semidirect
165. C₂×D₂₆₉	C₂×#41	semidirect
175. C₂×C₂₆₉	#546	semidirect
181. C₂₆₉	C₂×#546	semidirect
190. C₂×#121	D₂₆₉	semidirect
206. C₂²×D₄	C₂×D₂₆₉	semidirect
210. C₂³×C₄	C₂×D₂₆₉	semidirect
215. #121	C₂×D₂₆₉	semidirect
221. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
229. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
254. C₂×D₄	C₂²×D₂₆₉	semidirect
269. C₂²×C₄	C₂²×D₂₆₉	semidirect
272. C₄⋊C₄	C₂²×D₂₆₉	semidirect
279. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
359. C₂	#31771252	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×#16864402	2
C₂²×D₄×D₂₆₉	2
#31771252	2
C₂×#22575440	2
C₂×#22575435	2
C₂×#22575433	2
C₂×#22575424	2
C₂×#22575421	2
C₂×#22575415	2
C₂×C₄×C₂²⋊D₂₆₉	2
C₂×C₂²⋊C₄×D₂₆₉	2
C₂×#121×C₂₆₉	2
C₂×#546	269

Subgroups — C2×#31771252 #46824337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31771252 #46824337