Subgroups — C₄×#22575498 #46824090

Order 34432.

1660 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575498	C₂	1	1	yes	maximal, characteristic
2	#31771086	C₂	1	2	yes	maximal, complemented
3	#31771084	C₂	1	4	yes	maximal, complemented
4	#31771080	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771078	C₂	1	4	yes	maximal, complemented
6	#31771077	C₂	1	4	yes	maximal, complemented
7	C₄×#16864402	C₂	1	2	yes	maximal, complemented
8	C₄×#16864401	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₂²⋊D₂₆₉	C₂	1	4	yes	maximal, complemented
10	C₄×D₄×D₂₆₉	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×D₄×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#22575498	C₄	1	16	yes	direct product factor
13	C₂×#16864402	C₂²	1	2	yes	—
14	C₂×#16864401	C₂²	1	4	yes	—
15	C₂²×C₂²⋊D₂₆₉	C₂²	1	4	yes	—
16	C₂×D₄×D₂₆₉	C₂²	1	4	yes	—
17	C₂²×C₄×D₂₆₉	C₂²	1	4	yes	complemented
18	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
19	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
20	#22575418	C₂²	1	4	yes	complemented
21	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
22	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
23	D₄×Dic₂₆₉	C₂²	1	4	yes	complemented
24	D₄×Dic₂₆₉	C₂²	1	4	yes	complemented
25	#22575415	C₂²	1	4	yes	complemented
26	C₄×C₂²⋊D₂₆₉	C₂²	1	8	yes	complemented
27	C₄×C₂²⋊D₂₆₉	C₂²	1	4	yes	complemented
28	C₄×C₂²⋊D₂₆₉	C₂²	1	8	yes	complemented
29	C₄×C₂²⋊D₂₆₉	C₂²	1	8	yes	complemented
30	C₄×C₂²⋊D₂₆₉	C₂²	1	4	yes	complemented
31	#22575413	C₂²	1	8	yes	complemented
32	#22575413	C₂²	1	8	yes	complemented
33	#22575412	C₂²	1	2	yes	complemented
34	#22575411	C₂²	1	4	yes	complemented
35	#22575410	C₂²	1	4	yes	complemented
36	#22575409	C₂²	1	8	yes	complemented
37	C₂×#16864381	C₂²	1	4	yes	complemented
38	C₄⋊C₄×D₂₆₉	C₂²	1	4	yes	complemented
39	C₂×C₂²⋊Dic₂₆₉	C₂²	1	4	yes	complemented
40	C₂×#16864379	C₂²	1	4	yes	complemented
41	C₂²⋊C₄×D₂₆₉	C₂²	1	8	yes	complemented
42	C₂×C₄×Dic₂₆₉	C₂²	1	4	yes	complemented
43	C₄²×D₂₆₉	C₂²	1	4	yes	complemented
44	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
45	C₂³×C₄×C₂₆₉	C₂²	1	2	yes	complemented
46	C₄×D₄×C₂₆₉	C₂²	1	4	yes	complemented
47	C₄×D₄×C₂₆₉	C₂²	1	4	yes	complemented
48	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
50	C₂×C₄²×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
51	C₂³×D₂₆₉	C₂³	1	4	yes	—
52	#16864402	C₂×C₄	1	16	yes	complemented
53	#16864401	C₂×C₄	1	32	yes	complemented
54	C₂×Dic₅₃₈	C₂³	1	2	yes	—
55	C₂×D₁₀₇₆	C₂³	1	2	yes	—
56	C₂×C₂²⋊D₂₆₉	C₂×C₄	1	32	yes	complemented
57	C₂×C₂²⋊D₂₆₉	C₂³	1	8	yes	—
58	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
59	D₄×D₂₆₉	C₂×C₄	1	32	yes	complemented
60	C₂²×Dic₂₆₉	C₂³	1	4	yes	—
61	C₂²×Dic₂₆₉	C₂³	1	4	yes	—
62	C₂²×Dic₂₆₉	C₂³	1	4	yes	—
63	C₂×C₄×D₂₆₉	—	4	8	no	—
64	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
65	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
66	C₂×C₄×D₂₆₉	C₂³	1	8	yes	—
67	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
68	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
69	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
70	#16864381	C₂³	1	8	yes	—
71	#16864381	C₂³	1	4	yes	—
72	#16864381	C₂³	1	4	yes	—
73	C₂²⋊Dic₂₆₉	C₂³	1	8	yes	—
74	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
75	#16864379	C₂³	1	4	yes	—
76	#16864379	C₂³	1	8	yes	—
77	#16864379	C₂³	1	4	yes	—
78	C₄×Dic₂₆₉	C₂³	1	4	yes	—
79	C₄×Dic₂₆₉	C₂³	1	4	yes	—
80	C₄×Dic₂₆₉	C₂³	1	4	yes	—
81	C₄×Dic₂₆₉	C₂³	1	8	yes	—
82	C₂⁴×C₂₆₉	C₂³	1	2	yes	—
83	C₂×D₄×C₂₆₉	C₂×C₄	1	8	yes	complemented
84	C₂×D₄×C₂₆₉	C₂³	1	4	yes	—
85	C₂²×C₄×C₂₆₉	—	4	4	no	—
86	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	—
87	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	—
89	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
91	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
93	C₂²⋊C₄×C₂₆₉	C₂³	1	8	yes	—
94	C₄²×C₂₆₉	C₂³	1	2	yes	—
95	C₄²×C₂₆₉	C₂³	1	2	yes	—
96	C₂²×D₂₆₉	—	4	4	no	—
97	C₂²×D₂₆₉	—	4	4	no	—
98	C₂²×D₂₆₉	C₂²×C₄	1	16	yes	complemented
99	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
100	Dic₅₃₈	C₂²×C₄	1	8	yes	complemented
101	D₁₀₇₆	C₂²×C₄	1	8	yes	complemented
102	C₂²⋊D₂₆₉	C₂²×C₄	1	32	yes	complemented
103	C₂²⋊D₂₆₉	C₂²×C₄	1	16	yes	complemented
104	C₂×Dic₂₆₉	—	4	4	no	—
105	C₂×Dic₂₆₉	—	4	4	no	—
106	C₂×Dic₂₆₉	C₂²×C₄	1	16	yes	complemented
107	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
108	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
109	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
110	C₄×D₂₆₉	—	2	8	no	—
111	C₄×D₂₆₉	—	4	8	no	—
112	C₄×D₂₆₉	—	4	4	no	—
113	C₄×D₂₆₉	C₂²×C₄	1	16	yes	complemented
114	C₂³×C₂₆₉	—	4	2	no	—
115	C₂³×C₂₆₉	—	4	2	no	—
116	C₂³×C₂₆₉	C₂²×C₄	1	8	yes	complemented
117	C₂³×C₂₆₉	C₂⁴	1	4	yes	—
118	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
119	D₄×C₂₆₉	C₂²×C₄	1	16	yes	complemented
120	C₂×C₄×C₂₆₉	—	2	2	no	—
121	C₂×C₄×C₂₆₉	—	2	8	no	—
122	C₂×C₄×C₂₆₉	—	4	4	no	—
123	C₂×C₄×C₂₆₉	—	4	2	no	—
124	C₂×C₄×C₂₆₉	—	4	1	no	—
125	C₂×C₄×C₂₆₉	C₂²×C₄	1	4	yes	complemented
126	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
127	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
129	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
130	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
131	C₂²×C₂₆₉	—	2	1	no	—
132	C₂²×C₂₆₉	—	2	4	no	—
133	C₂²×C₂₆₉	—	2	1	no	—
134	C₂²×C₂₆₉	—	2	4	no	—
135	C₂²×C₂₆₉	—	4	8	no	—
136	C₂²×C₂₆₉	C₂³×C₄	1	2	yes	—
137	C₂²×C₂₆₉	C₂³×C₄	1	8	yes	—
138	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
139	C₂×D₂₆₉	—	2	4	no	—
140	C₂×D₂₆₉	—	2	4	no	—
141	C₂×D₂₆₉	—	4	16	no	—
142	C₂×D₂₆₉	C₂³×C₄	1	8	yes	—
143	C₄×C₂₆₉	—	2	1	no	—
144	C₄×C₂₆₉	—	2	4	no	—
145	C₄×C₂₆₉	—	2	2	no	—
146	C₄×C₂₆₉	C₂³×C₄	1	4	yes	—
147	C₄×C₂₆₉	H(5,𝔽₂)	1	2	yes	complemented
148	Dic₂₆₉	—	2	4	no	—
149	Dic₂₆₉	—	2	4	no	—
150	Dic₂₆₉	C₂³×C₄	1	8	yes	—
151	C₂×C₂₆₉	—	2	8	no	—
152	C₂×C₂₆₉	—	2	2	no	—
153	C₂×C₂₆₉	C₂⁴×C₄	1	1	yes	characteristic
154	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
155	C₂×C₂₆₉	#585	1	1	yes	characteristic
156	D₂₆₉	—	2	8	no	—
157	C₂₆₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
158	C₄×H(5,𝔽₂)	—	269	1	no	maximal, Sylow
159	C₂×H(5,𝔽₂)	—	269	1	no	—
160	#520	—	269	4	no	—
161	#520	—	269	2	no	—
162	#518	—	269	1	no	—
163	#518	—	269	4	no	—
164	#518	—	269	4	no	—
165	C₄×#41	—	269	4	no	—
166	C₄×#41	—	269	2	no	—
167	C₂×C₄×D₄	—	269	4	no	—
168	C₂×C₄×D₄	—	269	4	no	—
169	C₂×C₄×D₄	D₂₆₉	1	1	yes	characteristic, complemented
170	H(5,𝔽₂)	—	269	16	no	—
171	C₂×#41	—	269	4	no	—
172	C₂×#41	—	269	2	no	—
173	C₂²×D₄	—	269	4	no	—
174	C₂²×D₄	—	269	4	no	—
175	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic
176	C₂³×C₄	—	269	4	no	—
177	C₂³×C₄	C₂×D₂₆₉	1	2	yes	complemented
178	C₄×Q₈	—	269	4	no	—
179	C₄×Q₈	—	269	2	no	—
180	C₄×Q₈	—	269	2	no	—
181	C₄×D₄	—	269	4	no	—
182	C₄×D₄	—	269	4	no	—
183	C₄×D₄	—	269	8	no	—
184	C₄×D₄	—	269	4	no	—
185	C₄×D₄	—	269	8	no	—
186	C₄×D₄	—	269	8	no	—
187	C₄×D₄	—	269	4	no	—
188	C₄×D₄	—	269	4	no	—
189	C₄×D₄	—	269	8	no	—
190	C₄×D₄	—	269	8	no	—
191	C₄×D₄	—	269	2	no	—
192	C₄×D₄	—	269	2	no	—
193	C₄×D₄	C₂×D₂₆₉	1	4	yes	complemented
194	C₄×D₄	C₂×D₂₆₉	1	4	yes	complemented
195	#117	—	269	2	no	—
196	#117	—	269	4	no	—
197	#117	—	269	8	no	—
198	#117	—	269	4	no	—
199	C₂×C₄⋊C₄	—	269	4	no	—
200	C₂×C₄⋊C₄	—	269	4	no	—
201	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
202	C₂×C₂²⋊C₄	—	269	4	no	—
203	C₂×C₂²⋊C₄	—	269	4	no	—
204	C₂×C₂²⋊C₄	—	269	8	no	—
205	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
206	C₂×C₄²	—	269	4	no	—
207	C₂×C₄²	—	269	4	no	—
208	C₂×C₄²	C₂×D₂₆₉	1	1	yes	characteristic, complemented
209	C₂⁴	—	269	4	no	—
210	C₂⁴	C₂²×D₂₆₉	1	2	yes	—
211	#41	—	269	32	no	—
212	#41	—	269	16	no	—
213	C₂×Q₈	—	269	2	no	—
214	C₂×D₄	—	269	32	no	—
215	C₂×D₄	—	269	4	no	—
216	C₂×D₄	—	269	8	no	—
217	C₂×D₄	—	269	32	no	—
218	C₂×D₄	—	269	2	no	—
219	C₂×D₄	C₄×D₂₆₉	1	8	yes	complemented
220	C₂×D₄	C₂²×D₂₆₉	1	4	yes	—
221	C₂²×C₄	—	4	4	no	—
222	C₂²×C₄	—	269	4	no	—
223	C₂²×C₄	—	269	4	no	—
224	C₂²×C₄	—	269	4	no	—
225	C₂²×C₄	—	269	4	no	—
226	C₂²×C₄	—	269	4	no	—
227	C₂²×C₄	—	269	4	no	—
228	C₂²×C₄	—	269	8	no	—
229	C₂²×C₄	—	1076	8	no	—
230	C₂²×C₄	C₂²×D₂₆₉	1	4	yes	—
231	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
232	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
233	C₂²×C₄	C₂²×D₂₆₉	1	4	yes	—
234	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
235	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
236	C₄⋊C₄	—	269	8	no	—
237	C₄⋊C₄	—	269	4	no	—
238	C₄⋊C₄	—	269	2	no	—
239	C₄⋊C₄	—	269	4	no	—
240	C₄⋊C₄	—	269	2	no	—
241	C₄⋊C₄	C₂²×D₂₆₉	1	4	yes	—
242	C₂²⋊C₄	—	269	4	no	—
243	C₂²⋊C₄	—	269	8	no	—
244	C₂²⋊C₄	—	269	8	no	—
245	C₂²⋊C₄	—	269	4	no	—
246	C₂²⋊C₄	—	269	4	no	—
247	C₂²⋊C₄	C₂²×D₂₆₉	1	8	yes	—
248	C₄²	—	269	8	no	—
249	C₄²	—	269	4	no	—
250	C₄²	—	269	4	no	—
251	C₄²	—	269	4	no	—
252	C₄²	C₂²×D₂₆₉	1	2	yes	—
253	C₄²	C₂²×D₂₆₉	1	2	yes	—
254	C₂³	—	4	2	no	—
255	C₂³	—	4	2	no	—
256	C₂³	—	269	4	no	—
257	C₂³	—	269	16	no	—
258	C₂³	—	1076	4	no	—
259	C₂³	—	1076	4	no	—
260	C₂³	C₂×C₄×D₂₆₉	1	8	yes	complemented
261	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
262	C₂³	C₂³×D₂₆₉	1	4	yes	—
263	Q₈	—	269	8	no	—
264	D₄	—	269	32	no	—
265	D₄	—	269	16	no	—
266	D₄	—	269	8	no	—
267	D₄	C₂×C₄×D₂₆₉	1	16	yes	complemented
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	8	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	269	16	no	—
274	C₂×C₄	—	269	4	no	—
275	C₂×C₄	—	269	16	no	—
276	C₂×C₄	—	269	4	no	—
277	C₂×C₄	—	269	4	no	—
278	C₂×C₄	—	538	8	no	—
279	C₂×C₄	—	1076	8	no	—
280	C₂×C₄	—	1076	4	no	—
281	C₂×C₄	—	1076	4	no	—
282	C₂×C₄	—	1076	4	no	—
283	C₂×C₄	C₂×C₄×D₂₆₉	1	4	yes	complemented
284	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
285	C₂×C₄	C₂³×D₂₆₉	1	4	yes	—
286	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
287	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
288	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
289	C₂²	—	2	1	no	—
290	C₂²	—	2	4	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	2	4	no	—
293	C₂²	—	4	8	no	—
294	C₂²	—	269	8	no	—
295	C₂²	—	538	4	no	—
296	C₂²	—	538	4	no	—
297	C₂²	—	1076	16	no	—
298	C₂²	C₂²×C₄×D₂₆₉	1	8	yes	—
299	C₂²	C₂²×C₄×D₂₆₉	1	2	yes	—
300	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
301	C₄	—	2	1	no	—
302	C₄	—	2	4	no	—
303	C₄	—	2	2	no	—
304	C₄	—	269	8	no	—
305	C₄	—	538	4	no	—
306	C₄	—	538	4	no	—
307	C₄	C₂²×C₄×D₂₆₉	1	4	yes	—
308	C₄	#22575498	1	2	yes	direct product factor
309	C₂	—	2	2	no	—
310	C₂	—	2	8	no	—
311	C₂	—	538	8	no	—
312	C₂	C₂³×C₄×D₂₆₉	1	1	yes	characteristic
313	C₂	C₂×#22575498	1	1	yes	characteristic
314	C₂	#31771441	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₆₉
commutator	C₂×C₂₆₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₂₆₉
Fitting	C₂×C₄×D₄×C₂₆₉	C₂
socle, cosocle	C₂²×C₂₆₉	C₂⁵
prime radical	C₂×#22575498	C₂
hypercenter	C₂×C₄×D₄	D₂₆₉
hypocenter	C₂₆₉	C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #31771086	C₂	semidirect
3. #31771084	C₂	semidirect
4. #31771080	C₂	semidirect
5. #31771078	C₂	semidirect
6. #31771077	C₂	semidirect
7. C₄×#16864402	C₂	semidirect
8. C₄×#16864401	C₂	semidirect
9. C₂×C₄×C₂²⋊D₂₆₉	C₂	semidirect
10. C₄×D₄×D₂₆₉	C₂	semidirect
11. C₂×C₄×D₄×C₂₆₉	C₂	semidirect
12. #22575498	C₄	direct (N × H)
17. C₂²×C₄×D₂₆₉	C₂²	semidirect
18. C₄×Dic₅₃₈	C₂²	semidirect
19. C₄×Dic₅₃₈	C₂²	semidirect
20. #22575418	C₂²	semidirect
21. C₄×D₁₀₇₆	C₂²	semidirect
22. C₄×D₁₀₇₆	C₂²	semidirect
23. D₄×Dic₂₆₉	C₂²	semidirect
24. D₄×Dic₂₆₉	C₂²	semidirect
25. #22575415	C₂²	semidirect
26. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
27. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
28. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
29. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
30. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
31. #22575413	C₂²	semidirect
32. #22575413	C₂²	semidirect
33. #22575412	C₂²	semidirect
34. #22575411	C₂²	semidirect
35. #22575410	C₂²	semidirect
36. #22575409	C₂²	semidirect
37. C₂×#16864381	C₂²	semidirect
38. C₄⋊C₄×D₂₆₉	C₂²	semidirect
39. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
40. C₂×#16864379	C₂²	semidirect
41. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
42. C₂×C₄×Dic₂₆₉	C₂²	semidirect
43. C₄²×D₂₆₉	C₂²	semidirect
45. C₂³×C₄×C₂₆₉	C₂²	semidirect
46. C₄×D₄×C₂₆₉	C₂²	semidirect
47. C₄×D₄×C₂₆₉	C₂²	semidirect
48. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
49. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
50. C₂×C₄²×C₂₆₉	C₂²	semidirect
52. #16864402	C₂×C₄	semidirect
53. #16864401	C₂×C₄	semidirect
56. C₂×C₂²⋊D₂₆₉	C₂×C₄	semidirect
59. D₄×D₂₆₉	C₂×C₄	semidirect
83. C₂×D₄×C₂₆₉	C₂×C₄	semidirect
98. C₂²×D₂₆₉	C₂²×C₄	semidirect
100. Dic₅₃₈	C₂²×C₄	semidirect
101. D₁₀₇₆	C₂²×C₄	semidirect
102. C₂²⋊D₂₆₉	C₂²×C₄	semidirect
103. C₂²⋊D₂₆₉	C₂²×C₄	semidirect
106. C₂×Dic₂₆₉	C₂²×C₄	semidirect
113. C₄×D₂₆₉	C₂²×C₄	semidirect
116. C₂³×C₂₆₉	C₂²×C₄	semidirect
119. D₄×C₂₆₉	C₂²×C₄	semidirect
125. C₂×C₄×C₂₆₉	C₂²×C₄	semidirect
147. C₄×C₂₆₉	H(5,𝔽₂)	semidirect
157. C₂₆₉	C₄×H(5,𝔽₂)	semidirect
169. C₂×C₄×D₄	D₂₆₉	semidirect
177. C₂³×C₄	C₂×D₂₆₉	semidirect
193. C₄×D₄	C₂×D₂₆₉	semidirect
194. C₄×D₄	C₂×D₂₆₉	semidirect
201. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
205. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
208. C₂×C₄²	C₂×D₂₆₉	semidirect
219. C₂×D₄	C₄×D₂₆₉	semidirect
260. C₂³	C₂×C₄×D₂₆₉	semidirect
267. D₄	C₂×C₄×D₂₆₉	semidirect
283. C₂×C₄	C₂×C₄×D₂₆₉	semidirect
308. C₄	#22575498	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#22575498	2
#31771086	2
#31771084	2
#31771080	2
#31771078	2
#31771077	2
C₄×#16864402	2
C₄×#16864401	2
C₂×C₄×C₂²⋊D₂₆₉	2
C₄×D₄×D₂₆₉	2
C₂×C₄×D₄×C₂₆₉	2
C₄×H(5,𝔽₂)	269

Subgroups — C4×#22575498 #46824090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#22575498 #46824090