Subgroups — C₂²×#65400 #12963138

Order 1280.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
3	C₂³×#676	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#3952	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#65400	C₂	1	24	yes	maximal, direct product factor
7	C₂²×#3946	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#3947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₂²⋊D₅	C₄	1	1	yes	characteristic
11	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	—	2	8	no	—
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₅×C₈	C₂²	1	12	yes	complemented
16	C₂²×C₂²⋊Dic₅	C₄	1	1	yes	characteristic
17	C₂×C₄×C₂²⋊D₅	C₄	1	12	yes	—
18	C₂×C₄×C₂²⋊D₅	C₂²	1	12	yes	—
19	C₂²×#685	C₄	1	1	yes	characteristic
20	C₂²×#683	C₄	1	1	yes	characteristic
21	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂³×#168	C₂²	1	1	yes	characteristic
23	C₂³×#168	C₂²	1	1	yes	characteristic
24	C₂²×#676	—	2	8	no	—
25	C₂²×#676	C₂²	1	12	yes	complemented
26	C₂×C₂²⋊#168	C₂²	1	12	yes	complemented
27	#65400	C₂²	1	64	yes	direct product factor
28	C₂×#3952	C₂²	1	12	yes	complemented
29	C₂×#3947	C₂²	1	12	yes	complemented
30	C₂×#3946	C₂²	1	12	yes	complemented
31	C₂²×#435	—	5	1	no	maximal, Sylow
32	C₂⁵×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂⁴×D₅	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅	—	2	4	no	—
35	C₂³×C₄×C₅	—	2	4	no	—
36	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	C₂×C₄	1	6	yes	—
38	C₂³×C₄×C₅	C₂³	1	6	yes	—
39	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₂²⋊D₅	—	2	8	no	—
41	C₂²×C₂²⋊D₅	C₂×C₄	1	12	yes	—
42	C₂³×Dic₅	C₂×C₄	1	1	yes	characteristic
43	C₂³×Dic₅	C₂×C₄	1	1	yes	characteristic
44	C₂³×Dic₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₅	—	2	4	no	—
46	C₂²×C₄×D₅	—	2	4	no	—
47	C₂²×C₄×D₅	C₂×C₄	1	6	yes	—
48	C₂²×C₄×D₅	C₂³	1	6	yes	—
49	C₂²×C₅×C₈	—	2	4	no	—
50	C₂²×C₅×C₈	—	2	48	no	—
51	C₂²×C₅×C₈	D₄	1	8	yes	complemented
52	C₂²×C₅×C₈	C₂³	1	6	yes	—
53	C₂²×C₅×C₈	C₂³	1	6	yes	—
54	C₂²×C₅×C₈	C₂³	1	16	yes	complemented
55	C₂×C₂²⋊Dic₅	C₂×C₄	1	12	yes	—
56	C₄×C₂²⋊D₅	C₂×C₄	1	48	yes	—
57	C₄×C₂²⋊D₅	C₂³	1	16	yes	—
58	C₂×#685	C₂×C₄	1	12	yes	—
59	C₂×#683	C₂×C₄	1	12	yes	—
60	C₂×C₄×Dic₅	C₂×C₄	1	6	yes	—
61	C₂×C₄×Dic₅	C₂³	1	6	yes	—
62	C₂²×#168	—	2	4	no	—
63	C₂²×#168	—	2	4	no	—
64	C₂²×#168	C₂³	1	6	yes	—
65	C₂²×#168	C₂³	1	6	yes	—
66	C₂×#676	—	2	48	no	—
67	C₂×#676	C₂³	1	16	yes	complemented
68	C₂²⋊#168	C₂³	1	16	yes	complemented
69	#3952	C₂³	1	16	yes	complemented
70	#3947	C₂³	1	16	yes	complemented
71	#3946	C₂³	1	16	yes	complemented
72	C₂³×M₁₆	—	5	1	no	—
73	C₂⁴×C₈	D₅	1	1	yes	characteristic, complemented
74	C₂²×C₄×D₄	—	5	1	no	—
75	C₂×#435	—	5	24	no	—
76	C₂²×C₄⋊C₈	—	5	1	no	—
77	C₂²×C₂²⋊C₈	—	5	1	no	—
78	C₂²×C₂²⋊C₈	—	5	1	no	—
79	C₂²×#97	—	5	1	no	—
80	C₂⁴×C₅	—	2	4	no	—
81	C₂⁴×C₅	—	2	4	no	—
82	C₂⁴×C₅	M₁₆	1	8	yes	complemented
83	C₂⁴×C₅	C₂²×C₄	1	6	yes	—
84	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂³×D₅	—	2	4	no	—
86	C₂³×D₅	—	2	4	no	—
87	C₂³×D₅	—	2	4	no	—
88	C₂³×D₅	C₂²×C₄	1	6	yes	—
89	C₂²×C₄×C₅	—	2	4	no	—
90	C₂²×C₄×C₅	—	2	24	no	—
91	C₂²×C₄×C₅	—	2	12	no	—
92	C₂²×C₄×C₅	—	2	12	no	—
93	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	12	yes	—
95	C₂²×C₄×C₅	C₂²×C₄	1	3	yes	—
96	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₅	#41	1	4	yes	—
98	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
99	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
100	C₂×C₂²⋊D₅	—	2	48	no	—
101	C₂×C₂²⋊D₅	C₂²×C₄	1	16	yes	—
102	C₂²×Dic₅	—	2	4	no	—
103	C₂²×Dic₅	—	2	4	no	—
104	C₂²×Dic₅	—	2	4	no	—
105	C₂²×Dic₅	C₂²×C₄	1	6	yes	—
106	C₂²×Dic₅	C₂²×C₄	1	6	yes	—
107	C₂²×Dic₅	C₂²×C₄	1	6	yes	—
108	C₂×C₄×D₅	—	2	24	no	—
109	C₂×C₄×D₅	—	2	12	no	—
110	C₂×C₄×D₅	—	2	12	no	—
111	C₂×C₄×D₅	C₂²×C₄	1	12	yes	—
112	C₂×C₄×D₅	C₂⁴	1	4	yes	—
113	C₂×C₅×C₈	—	2	12	no	—
114	C₂×C₅×C₈	—	2	32	no	—
115	C₂×C₅×C₈	C₂×D₄	1	24	yes	complemented
116	C₂×C₅×C₈	C₂⁴	1	4	yes	—
117	C₂×C₅×C₈	C₂⁴	1	4	yes	—
118	C₂²⋊Dic₅	C₂²×C₄	1	16	yes	—
119	#685	C₂²×C₄	1	16	yes	—
120	#683	C₂²×C₄	1	16	yes	—
121	C₄×Dic₅	C₂²×C₄	1	12	yes	—
122	C₄×Dic₅	C₂⁴	1	4	yes	—
123	C₂×#168	—	2	12	no	—
124	C₂×#168	—	2	12	no	—
125	C₂×#168	C₂⁴	1	4	yes	—
126	C₂×#168	C₂⁴	1	4	yes	—
127	#676	—	2	32	no	—
128	C₂³×D₄	—	5	1	no	—
129	C₂⁴×C₄	—	5	1	no	—
130	C₂⁴×C₄	C₂×D₅	1	1	yes	characteristic
131	C₂²×M₁₆	—	5	12	no	—
132	C₂²×M₁₆	—	10	8	no	—
133	C₂³×C₈	—	2	8	no	—
134	C₂³×C₈	—	5	1	no	—
135	C₂³×C₈	—	5	1	no	—
136	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
137	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
138	C₂³×C₈	C₂×D₅	1	12	yes	complemented
139	C₂×C₄×D₄	—	5	12	no	—
140	C₂×C₄×D₄	—	5	12	no	—
141	C₂²×C₄⋊C₄	—	5	1	no	—
142	C₂²×C₂²⋊C₄	—	5	1	no	—
143	C₂²×C₂²⋊C₄	—	5	1	no	—
144	C₂²×C₄²	—	5	1	no	—
145	#435	—	5	64	no	—
146	C₂×C₄⋊C₈	—	5	12	no	—
147	C₂×C₂²⋊C₈	—	5	12	no	—
148	C₂×C₂²⋊C₈	—	5	12	no	—
149	C₂×#97	—	5	12	no	—
150	C₂³×C₅	—	2	12	no	—
151	C₂³×C₅	—	2	12	no	—
152	C₂³×C₅	—	2	32	no	—
153	C₂³×C₅	C₄×D₄	1	4	yes	—
154	C₂³×C₅	C₂×M₁₆	1	4	yes	—
155	C₂³×C₅	C₂×M₁₆	1	24	yes	complemented
156	C₂³×C₅	#131	1	4	yes	—
157	C₂³×C₅	C₂³×C₄	1	4	yes	—
158	C₂³×C₅	C₂³×C₄	1	3	yes	—
159	C₂²×D₅	—	2	12	no	—
160	C₂²×D₅	—	2	12	no	—
161	C₂²×D₅	—	2	12	no	—
162	C₂²×D₅	—	4	16	no	—
163	C₂²×D₅	C₂³×C₄	1	4	yes	—
164	C₂×C₄×C₅	—	2	12	no	—
165	C₂×C₄×C₅	—	2	24	no	—
166	C₂×C₄×C₅	—	2	4	no	—
167	C₂×C₄×C₅	—	2	4	no	—
168	C₂×C₄×C₅	C₄×D₄	1	12	yes	—
169	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
170	C₂×C₄×C₅	C₂³×C₄	1	3	yes	—
171	C₂×C₄×C₅	C₂²×D₄	1	6	yes	—
172	C₂×C₄×C₅	C₂×#41	1	6	yes	—
173	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
174	C₂²⋊D₅	—	2	32	no	—
175	C₂×Dic₅	—	2	12	no	—
176	C₂×Dic₅	—	2	12	no	—
177	C₂×Dic₅	—	2	12	no	—
178	C₂×Dic₅	C₂³×C₄	1	4	yes	—
179	C₂×Dic₅	C₂³×C₄	1	4	yes	—
180	C₂×Dic₅	C₂³×C₄	1	4	yes	—
181	C₄×D₅	—	2	24	no	—
182	C₄×D₅	—	2	4	no	—
183	C₄×D₅	—	2	4	no	—
184	C₅×C₈	—	2	4	no	—
185	C₅×C₈	C₂²×D₄	1	8	yes	complemented
186	#168	—	2	4	no	—
187	#168	—	2	4	no	—
188	C₂⁵	—	5	1	no	—
189	C₂⁵	C₄×D₅	1	1	yes	characteristic
190	C₂²×D₄	—	5	12	no	—
191	C₂²×D₄	—	10	8	no	—
192	C₂³×C₄	—	2	4	no	—
193	C₂³×C₄	—	2	4	no	—
194	C₂³×C₄	—	5	1	no	—
195	C₂³×C₄	—	5	1	no	—
196	C₂³×C₄	—	5	1	no	—
197	C₂³×C₄	—	5	6	no	—
198	C₂³×C₄	—	5	6	no	—
199	C₂³×C₄	—	10	4	no	—
200	C₂³×C₄	—	10	4	no	—
201	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
202	C₂³×C₄	C₄×D₅	1	6	yes	—
203	C₂³×C₄	C₂²×D₅	1	6	yes	—
204	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
205	C₂×M₁₆	—	5	16	no	—
206	C₂×M₁₆	—	10	48	no	—
207	C₂²×C₈	—	2	4	no	—
208	C₂²×C₈	—	2	48	no	—
209	C₂²×C₈	—	5	6	no	—
210	C₂²×C₈	—	5	6	no	—
211	C₂²×C₈	—	10	4	no	—
212	C₂²×C₈	—	10	4	no	—
213	C₂²×C₈	C₂²⋊D₅	1	8	yes	complemented
214	C₂²×C₈	C₂²×D₅	1	6	yes	—
215	C₂²×C₈	C₂²×D₅	1	6	yes	—
216	C₂²×C₈	C₂²×D₅	1	16	yes	complemented
217	C₄×D₄	—	5	48	no	—
218	C₄×D₄	—	5	16	no	—
219	C₂×C₄⋊C₄	—	5	12	no	—
220	C₂×C₂²⋊C₄	—	5	12	no	—
221	C₂×C₂²⋊C₄	—	5	12	no	—
222	C₂×C₄²	—	5	6	no	—
223	C₂×C₄²	—	5	6	no	—
224	C₄⋊C₈	—	5	16	no	—
225	C₂²⋊C₈	—	5	16	no	—
226	C₂²⋊C₈	—	5	16	no	—
227	#97	—	5	16	no	—
228	C₂²×C₅	—	2	4	no	—
229	C₂²×C₅	—	2	48	no	—
230	C₂²×C₅	—	2	4	no	—
231	C₂²×C₅	#435	1	16	yes	complemented
232	C₂²×C₅	C₂×C₄×D₄	1	6	yes	—
233	C₂²×C₅	C₂²×M₁₆	1	6	yes	—
234	C₂²×C₅	C₂²×M₁₆	1	8	yes	complemented
235	C₂²×C₅	C₂×#131	1	6	yes	—
236	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
237	C₂×D₅	—	2	4	no	—
238	C₂×D₅	—	2	4	no	—
239	C₂×D₅	—	2	4	no	—
240	C₂×D₅	—	4	24	no	—
241	C₄×C₅	—	2	4	no	—
242	C₄×C₅	C₂×C₄×D₄	1	6	yes	—
243	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
244	C₄×C₅	C₂²×#41	1	1	yes	characteristic
245	Dic₅	—	2	4	no	—
246	Dic₅	—	2	4	no	—
247	Dic₅	—	2	4	no	—
248	C₂⁴	—	2	4	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	5	6	no	—
251	C₂⁴	—	10	4	no	—
252	C₂⁴	—	10	4	no	—
253	C₂⁴	—	10	4	no	—
254	C₂⁴	#676	1	8	yes	complemented
255	C₂⁴	C₂×C₄×D₅	1	6	yes	—
256	C₂⁴	C₂×C₄×D₅	1	1	yes	characteristic
257	C₂×D₄	—	5	16	no	—
258	C₂×D₄	—	10	48	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	12	no	—
261	C₂²×C₄	—	2	12	no	—
262	C₂²×C₄	—	2	24	no	—
263	C₂²×C₄	—	5	6	no	—
264	C₂²×C₄	—	5	6	no	—
265	C₂²×C₄	—	5	6	no	—
266	C₂²×C₄	—	5	12	no	—
267	C₂²×C₄	—	5	4	no	—
268	C₂²×C₄	—	10	4	no	—
269	C₂²×C₄	—	10	4	no	—
270	C₂²×C₄	—	10	4	no	—
271	C₂²×C₄	—	10	12	no	—
272	C₂²×C₄	—	10	12	no	—
273	C₂²×C₄	—	10	24	no	—
274	C₂²×C₄	C₂×C₄×D₅	1	6	yes	—
275	C₂²×C₄	C₂×C₄×D₅	1	12	yes	—
276	C₂²×C₄	C₂×C₄×D₅	1	3	yes	—
277	C₂²×C₄	#709	1	4	yes	—
278	C₂²×C₄	C₂×C₂²⋊D₅	1	4	yes	—
279	C₂²×C₄	C₂³×D₅	1	4	yes	—
280	C₂²×C₄	C₂³×D₅	1	3	yes	—
281	M₁₆	—	10	32	no	—
282	C₂×C₈	—	2	12	no	—
283	C₂×C₈	—	2	32	no	—
284	C₂×C₈	—	5	4	no	—
285	C₂×C₈	—	5	4	no	—
286	C₂×C₈	—	10	12	no	—
287	C₂×C₈	—	10	12	no	—
288	C₂×C₈	C₂×C₂²⋊D₅	1	24	yes	complemented
289	C₂×C₈	C₂³×D₅	1	4	yes	—
290	C₂×C₈	C₂³×D₅	1	4	yes	—
291	C₄⋊C₄	—	5	16	no	—
292	C₂²⋊C₄	—	5	16	no	—
293	C₂²⋊C₄	—	5	16	no	—
294	C₄²	—	5	12	no	—
295	C₄²	—	5	4	no	—
296	C₂×C₅	—	2	8	no	—
297	C₂×C₅	C₂×#435	1	12	yes	complemented
298	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
299	C₂×C₅	C₂³×M₁₆	1	1	yes	characteristic
300	C₂×C₅	C₂²×#131	1	1	yes	characteristic
301	D₅	—	4	4	no	—
302	C₂³	—	2	12	no	—
303	C₂³	—	2	12	no	—
304	C₂³	—	2	32	no	—
305	C₂³	—	5	4	no	—
306	C₂³	—	10	12	no	—
307	C₂³	—	10	12	no	—
308	C₂³	—	10	12	no	—
309	C₂³	—	20	16	no	—
310	C₂³	C₂×#676	1	4	yes	—
311	C₂³	C₂×#676	1	24	yes	complemented
312	C₂³	#4047	1	4	yes	—
313	C₂³	C₄×C₂²⋊D₅	1	4	yes	—
314	C₂³	C₂²×C₄×D₅	1	4	yes	—
315	C₂³	C₂²×C₄×D₅	1	3	yes	—
316	D₄	—	10	32	no	—
317	C₂×C₄	—	2	12	no	—
318	C₂×C₄	—	2	24	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	5	4	no	—
322	C₂×C₄	—	5	4	no	—
323	C₂×C₄	—	5	4	no	—
324	C₂×C₄	—	10	12	no	—
325	C₂×C₄	—	10	12	no	—
326	C₂×C₄	—	10	12	no	—
327	C₂×C₄	—	10	24	no	—
328	C₂×C₄	—	10	4	no	—
329	C₂×C₄	—	10	4	no	—
330	C₂×C₄	C₄×C₂²⋊D₅	1	12	yes	—
331	C₂×C₄	C₂²×C₄×D₅	1	4	yes	—
332	C₂×C₄	C₂²×C₄×D₅	1	3	yes	—
333	C₂×C₄	C₂×#709	1	6	yes	—
334	C₂×C₄	C₂²×C₂²⋊D₅	1	6	yes	—
335	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
336	C₈	—	2	4	no	—
337	C₈	—	10	4	no	—
338	C₈	—	10	4	no	—
339	C₈	C₂²×C₂²⋊D₅	1	8	yes	complemented
340	C₅	C₂²×#435	1	1	yes	characteristic, complemented, Sylow
341	C₂²	—	2	4	no	—
342	C₂²	—	2	48	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	10	4	no	—
345	C₂²	—	10	4	no	—
346	C₂²	—	10	4	no	—
347	C₂²	—	20	24	no	—
348	C₂²	#65400	1	16	yes	direct product factor
349	C₂²	C₂²×#676	1	6	yes	—
350	C₂²	C₂²×#676	1	8	yes	complemented
351	C₂²	C₂×#4047	1	6	yes	—
352	C₂²	C₂×C₄×C₂²⋊D₅	1	6	yes	—
353	C₂²	C₂³×C₄×D₅	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	10	4	no	—
356	C₄	—	10	4	no	—
357	C₄	—	10	4	no	—
358	C₄	C₂×C₄×C₂²⋊D₅	1	6	yes	—
359	C₄	C₂²×#709	1	1	yes	characteristic
360	C₄	C₂³×C₂²⋊D₅	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	20	4	no	—
363	C₂	C₂×#65400	1	12	yes	direct product factor
364	C₂	C₂³×#676	1	1	yes	characteristic
365	C₂	C₂²×#4047	1	1	yes	characteristic
366	C₂	C₂²×C₄×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₅
Fitting	C₂⁴×C₅×C₈	C₂
socle	C₂⁴×C₅	C₂²×C₄
prime radical	C₂³×C₂²⋊D₅	C₄
cosocle	C₂×C₄×C₅	C₂⁵
hypercenter	C₂⁴×C₈	D₅
hypocenter	C₅	C₂²×#435
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁴×C₈

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×C₈	C₂	semidirect
3. C₂³×#676	C₂	semidirect
4. C₂²×C₂²⋊#168	C₂	semidirect
5. C₂²×#3952	C₂	semidirect
6. C₂×#65400	C₂	direct (N × H)
7. C₂²×#3946	C₂	semidirect
8. C₂²×#3947	C₂	semidirect
15. C₂³×C₅×C₈	C₂²	semidirect
25. C₂²×#676	C₂²	semidirect
26. C₂×C₂²⋊#168	C₂²	semidirect
27. #65400	C₂²	direct (N × H)
28. C₂×#3952	C₂²	semidirect
29. C₂×#3947	C₂²	semidirect
30. C₂×#3946	C₂²	semidirect
51. C₂²×C₅×C₈	D₄	semidirect
54. C₂²×C₅×C₈	C₂³	semidirect
67. C₂×#676	C₂³	semidirect
68. C₂²⋊#168	C₂³	semidirect
69. #3952	C₂³	semidirect
70. #3947	C₂³	semidirect
71. #3946	C₂³	semidirect
73. C₂⁴×C₈	D₅	semidirect
82. C₂⁴×C₅	M₁₆	semidirect
115. C₂×C₅×C₈	C₂×D₄	semidirect
138. C₂³×C₈	C₂×D₅	semidirect
155. C₂³×C₅	C₂×M₁₆	semidirect
185. C₅×C₈	C₂²×D₄	semidirect
213. C₂²×C₈	C₂²⋊D₅	semidirect
216. C₂²×C₈	C₂²×D₅	semidirect
231. C₂²×C₅	#435	semidirect
234. C₂²×C₅	C₂²×M₁₆	semidirect
254. C₂⁴	#676	semidirect
288. C₂×C₈	C₂×C₂²⋊D₅	semidirect
297. C₂×C₅	C₂×#435	semidirect
311. C₂³	C₂×#676	semidirect
339. C₈	C₂²×C₂²⋊D₅	semidirect
340. C₅	C₂²×#435	semidirect
348. C₂²	#65400	direct (N × H)
350. C₂²	C₂²×#676	semidirect
363. C₂	C₂×#65400	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×C₈	2
C₂²×C₄×C₂²⋊D₅	2
C₂³×#676	2
C₂²×C₂²⋊#168	2
C₂²×#3952	2
C₂×#65400	2
C₂²×#3946	2
C₂²×#3947	2
C₂²×#435	5

Subgroups — C22×#65400 #12963138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#65400 #12963138