Subgroups — C₂×C₅×#2168 #11956150

Order 1280.

754 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#2168	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
12	C₂×C₅×M₃₂	—	2	4	no	—
13	C₂×C₅×M₃₂	C₂²	1	4	yes	complemented
14	C₂²×C₅×C₁₆	—	2	4	no	—
15	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₁₆	C₂²	1	4	yes	complemented
20	C₅×C₈×D₄	C₄	1	4	yes	—
21	C₅×C₈×D₄	C₂²	1	4	yes	—
22	C₂×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₅×C₄⋊C₁₆	C₂²	1	4	yes	complemented
27	C₅×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
28	C₅×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
29	C₅×#346	C₂²	1	4	yes	complemented
30	C₂×#2168	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂²×C₅×D₄	C₈	1	1	yes	characteristic
32	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₅×C₈	—	2	2	no	—
35	C₂²×C₅×C₈	—	2	2	no	—
36	C₂²×C₅×C₈	—	2	2	no	—
37	C₂²×C₅×C₈	—	2	2	no	—
38	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₄×C₅×D₄	C₈	1	4	yes	—
47	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
48	C₂×C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
49	C₂×C₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
50	C₂×C₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₅×M₃₂	—	2	8	no	—
53	C₂×C₅×C₁₆	—	2	2	no	—
54	C₂×C₅×C₁₆	—	2	2	no	—
55	C₂×C₅×C₁₆	—	2	2	no	—
56	C₂×C₅×C₁₆	—	2	8	no	—
57	C₂×C₅×C₁₆	D₄	1	4	yes	complemented
58	C₂×C₅×C₁₆	C₂³	1	2	yes	—
59	C₂×C₅×C₁₆	C₂³	1	2	yes	—
60	C₂×C₅×C₁₆	C₂³	1	2	yes	—
61	C₂×C₅×C₁₆	C₂³	1	2	yes	—
62	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
64	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
65	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
66	C₄×C₅×C₈	C₂³	1	2	yes	—
67	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂³×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic
70	#2168	C₂×C₅	1	8	yes	direct product factor
71	C₂×C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#346	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
76	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
77	C₂×C₅×D₄	—	2	4	no	—
78	C₂×C₅×D₄	C₂×C₈	1	4	yes	—
79	C₂²×C₄×C₅	—	2	2	no	—
80	C₂²×C₄×C₅	—	2	2	no	—
81	C₂²×C₄×C₅	—	2	2	no	—
82	C₂²×C₄×C₅	—	2	2	no	—
83	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
88	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
89	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₅×C₈	—	2	2	no	—
93	C₂×C₅×C₈	—	2	2	no	—
94	C₂×C₅×C₈	—	2	2	no	—
95	C₂×C₅×C₈	—	2	4	no	—
96	C₂×C₅×C₈	—	2	4	no	—
97	C₂×C₅×C₈	—	2	2	no	—
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	—	2	2	no	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
102	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
103	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
106	C₂×C₅×C₈	#41	1	2	yes	—
107	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
108	C₅×C₄⋊C₄	C₂×C₈	1	4	yes	—
109	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	—
110	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	—
111	C₄²×C₅	C₂×C₈	1	2	yes	—
112	C₄²×C₅	C₂²×C₄	1	2	yes	—
113	C₅×C₁₆	—	2	2	no	—
114	C₅×C₁₆	—	2	2	no	—
115	C₅×C₁₆	—	2	2	no	—
116	C₅×C₁₆	C₂×D₄	1	4	yes	complemented
117	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
118	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
120	C₂×M₃₂	—	2	4	no	—
121	C₂×M₃₂	C₂²×C₅	1	4	yes	complemented
122	C₂²×C₁₆	—	2	4	no	—
123	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
124	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
125	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
126	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
127	C₂²×C₁₆	C₂²×C₅	1	4	yes	complemented
128	C₈×D₄	C₄×C₅	1	4	yes	—
129	C₈×D₄	C₂²×C₅	1	4	yes	—
130	C₂×C₄⋊C₈	C₄×C₅	1	1	yes	characteristic
131	C₂×C₂²⋊C₈	C₄×C₅	1	1	yes	characteristic
132	C₂×C₂²⋊C₈	C₄×C₅	1	1	yes	characteristic
133	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
134	C₄⋊C₁₆	C₂²×C₅	1	4	yes	complemented
135	C₂²⋊C₁₆	C₂²×C₅	1	4	yes	complemented
136	C₂²⋊C₁₆	C₂²×C₅	1	4	yes	complemented
137	#346	C₂²×C₅	1	4	yes	complemented
138	C₂³×C₅	—	2	2	no	—
139	C₂³×C₅	—	2	2	no	—
140	C₂³×C₅	—	2	2	no	—
141	C₂³×C₅	—	2	2	no	—
142	C₂³×C₅	—	2	2	no	—
143	C₂³×C₅	M₃₂	1	4	yes	complemented
144	C₂³×C₅	C₂²×C₈	1	2	yes	—
145	C₂³×C₅	C₂²×C₈	1	2	yes	—
146	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
147	C₅×D₄	—	2	8	no	—
148	C₂×C₄×C₅	—	2	2	no	—
149	C₂×C₄×C₅	—	2	2	no	—
150	C₂×C₄×C₅	—	2	2	no	—
151	C₂×C₄×C₅	—	2	2	no	—
152	C₂×C₄×C₅	—	2	2	no	—
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	4	no	—
157	C₂×C₄×C₅	—	2	4	no	—
158	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
160	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
161	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
163	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₅	#131	1	2	yes	—
165	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₅×C₈	—	2	2	no	—
167	C₅×C₈	—	2	2	no	—
168	C₅×C₈	—	2	2	no	—
169	C₅×C₈	C₄×D₄	1	2	yes	—
170	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
171	C₅×C₈	C₂×#41	1	1	yes	characteristic
172	C₂²×D₄	C₅×C₈	1	1	yes	characteristic
173	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
174	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
175	C₂²×C₈	—	2	2	no	—
176	C₂²×C₈	—	2	2	no	—
177	C₂²×C₈	—	2	2	no	—
178	C₂²×C₈	—	2	2	no	—
179	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
180	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
181	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
182	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
183	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
184	C₂²×C₈	C₂³×C₅	1	2	yes	—
185	C₂²×C₈	C₂³×C₅	1	2	yes	—
186	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
187	C₄×D₄	C₅×C₈	1	4	yes	—
188	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
189	C₂×C₄⋊C₄	C₅×C₈	1	1	yes	characteristic
190	C₂×C₂²⋊C₄	C₅×C₈	1	1	yes	characteristic
191	C₂×C₂²⋊C₄	C₅×C₈	1	1	yes	characteristic
192	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
193	M₃₂	—	2	8	no	—
194	C₂×C₁₆	—	2	2	no	—
195	C₂×C₁₆	—	2	2	no	—
196	C₂×C₁₆	—	2	2	no	—
197	C₂×C₁₆	—	2	8	no	—
198	C₂×C₁₆	C₅×D₄	1	4	yes	complemented
199	C₂×C₁₆	C₂³×C₅	1	2	yes	—
200	C₂×C₁₆	C₂³×C₅	1	2	yes	—
201	C₂×C₁₆	C₂³×C₅	1	2	yes	—
202	C₂×C₁₆	C₂³×C₅	1	2	yes	—
203	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
204	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
205	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
206	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
207	C₄×C₈	C₂³×C₅	1	2	yes	—
208	C₂²×C₅	—	2	2	no	—
209	C₂²×C₅	—	2	2	no	—
210	C₂²×C₅	—	2	8	no	—
211	C₂²×C₅	—	2	2	no	—
212	C₂²×C₅	—	2	2	no	—
213	C₂²×C₅	—	2	2	no	—
214	C₂²×C₅	—	4	4	no	—
215	C₂²×C₅	C₈×D₄	1	2	yes	—
216	C₂²×C₅	C₂×M₃₂	1	2	yes	—
217	C₂²×C₅	C₂×M₃₂	1	4	yes	complemented
218	C₂²×C₅	#504	1	2	yes	—
219	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
220	C₄×C₅	—	2	2	no	—
221	C₄×C₅	—	2	2	no	—
222	C₄×C₅	—	2	2	no	—
223	C₄×C₅	—	2	2	no	—
224	C₄×C₅	C₈×D₄	1	2	yes	—
225	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₅	C₂×#131	1	1	yes	characteristic
227	C₂⁴	C₂×C₅×C₈	1	1	yes	characteristic
228	C₂⁴	C₂×C₅×C₈	1	1	yes	characteristic
229	C₂×D₄	—	2	4	no	—
230	C₂×D₄	C₂×C₅×C₈	1	4	yes	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
236	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
237	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
238	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
239	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
240	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
243	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
254	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
255	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
256	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
257	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
258	C₂×C₈	C₅×#41	1	2	yes	—
259	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
260	C₄⋊C₄	C₂×C₅×C₈	1	4	yes	—
261	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	—
262	C₂²⋊C₄	C₂×C₅×C₈	1	4	yes	—
263	C₄²	C₂×C₅×C₈	1	2	yes	—
264	C₄²	C₂²×C₄×C₅	1	2	yes	—
265	C₁₆	—	2	2	no	—
266	C₁₆	—	2	2	no	—
267	C₁₆	—	2	2	no	—
268	C₁₆	C₂×C₅×D₄	1	4	yes	complemented
269	C₂×C₅	—	2	4	no	—
270	C₂×C₅	—	4	2	no	—
271	C₂×C₅	#2168	1	4	yes	direct product factor
272	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
273	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
274	C₂×C₅	C₂×#504	1	1	yes	characteristic
275	C₂³	—	2	2	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	2	no	—
280	C₂³	C₅×M₃₂	1	4	yes	complemented
281	C₂³	C₂²×C₅×C₈	1	2	yes	—
282	C₂³	C₂²×C₅×C₈	1	2	yes	—
283	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
284	D₄	—	2	8	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
296	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
297	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
298	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
299	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
300	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
301	C₂×C₄	C₅×#131	1	2	yes	—
302	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
303	C₈	—	2	2	no	—
304	C₈	—	2	2	no	—
305	C₈	—	2	2	no	—
306	C₈	C₄×C₅×D₄	1	2	yes	—
307	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
308	C₈	C₂×C₅×#41	1	1	yes	characteristic
309	C₅	C₂×#2168	1	1	yes	characteristic, direct product factor, Sylow
310	C₂²	—	2	8	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	4	4	no	—
317	C₂²	C₅×C₈×D₄	1	2	yes	—
318	C₂²	C₂×C₅×M₃₂	1	2	yes	—
319	C₂²	C₂×C₅×M₃₂	1	4	yes	complemented
320	C₂²	C₅×#504	1	2	yes	—
321	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	C₅×C₈×D₄	1	2	yes	—
327	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
328	C₄	C₂×C₅×#131	1	1	yes	characteristic
329	C₂	—	2	4	no	—
330	C₂	—	4	2	no	—
331	C₂	C₅×#2168	1	4	yes	direct product factor
332	C₂	C₂×C₅×C₈×D₄	1	1	yes	characteristic
333	C₂	C₂²×C₅×M₃₂	1	1	yes	characteristic
334	C₂	C₂×C₅×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅×C₈	C₂³
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂³×C₅	C₂²×C₈
prime radical	C₂²×C₅×D₄	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×M₃₂	C₂	semidirect
2. C₂³×C₅×C₁₆	C₂	semidirect
4. C₅×#2168	C₂	direct (N × H)
5. C₂×C₅×C₄⋊C₁₆	C₂	semidirect
6. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
7. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
8. C₂×C₅×#346	C₂	semidirect
13. C₂×C₅×M₃₂	C₂²	semidirect
19. C₂²×C₅×C₁₆	C₂²	semidirect
26. C₅×C₄⋊C₁₆	C₂²	semidirect
27. C₅×C₂²⋊C₁₆	C₂²	semidirect
28. C₅×C₂²⋊C₁₆	C₂²	semidirect
29. C₅×#346	C₂²	semidirect
30. C₂×#2168	C₅	direct (N × H)
57. C₂×C₅×C₁₆	D₄	semidirect
67. C₂²×M₃₂	C₂×C₅	semidirect
68. C₂³×C₁₆	C₂×C₅	semidirect
70. #2168	C₂×C₅	direct (N × H)
71. C₂×C₄⋊C₁₆	C₂×C₅	semidirect
72. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
73. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
74. C₂×#346	C₂×C₅	semidirect
116. C₅×C₁₆	C₂×D₄	semidirect
121. C₂×M₃₂	C₂²×C₅	semidirect
127. C₂²×C₁₆	C₂²×C₅	semidirect
134. C₄⋊C₁₆	C₂²×C₅	semidirect
135. C₂²⋊C₁₆	C₂²×C₅	semidirect
136. C₂²⋊C₁₆	C₂²×C₅	semidirect
137. #346	C₂²×C₅	semidirect
143. C₂³×C₅	M₃₂	semidirect
198. C₂×C₁₆	C₅×D₄	semidirect
217. C₂²×C₅	C₂×M₃₂	semidirect
268. C₁₆	C₂×C₅×D₄	semidirect
271. C₂×C₅	#2168	direct (N × H)
280. C₂³	C₅×M₃₂	semidirect
309. C₅	C₂×#2168	direct (N × H)
319. C₂²	C₂×C₅×M₃₂	semidirect
331. C₂	C₅×#2168	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×C₅×M₃₂	2
C₂³×C₅×C₁₆	2
C₂×C₅×C₈×D₄	2
C₅×#2168	2
C₂×C₅×C₄⋊C₁₆	2
C₂×C₅×C₂²⋊C₁₆	2
C₂×C₅×#346	2
C₂×#2168	5

Subgroups — C2×C5×#2168 #11956150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2168 #11956150