Subgroups — C₅×#22992 #11945712

Order 1280.

1026 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2392	C₂	1	1	yes	maximal, characteristic
6	C₅×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₅×#117	C₂²	1	1	yes	characteristic
24	C₅×#436	—	2	4	no	—
25	C₅×#435	—	2	4	no	—
26	C₅×C₈×D₄	—	2	4	no	—
27	C₅×#424	—	2	4	no	—
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₅×#97	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
46	C₅×#398	C₄	1	1	yes	characteristic
47	C₅×#397	C₄	1	1	yes	characteristic
48	C₅×#396	C₄	1	1	yes	characteristic
49	C₅×#396	C₄	1	1	yes	characteristic
50	C₅×#394	C₄	1	1	yes	characteristic
51	C₅×#394	C₄	1	1	yes	characteristic
52	C₅×#394	C₄	1	1	yes	characteristic
53	C₅×#392	C₄	1	1	yes	characteristic
54	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	C₅×#336	C₂²	1	1	yes	characteristic
63	#22992	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₅×M₁₆	—	2	2	no	—
71	C₂×C₅×M₁₆	—	2	2	no	—
72	C₂×C₅×M₁₆	—	2	2	no	—
73	C₂×C₅×M₁₆	—	2	2	no	—
74	C₂×C₅×M₁₆	—	4	1	no	—
75	C₂×C₅×M₁₆	—	4	1	no	—
76	C₂²×C₅×C₈	—	2	2	no	—
77	C₂²×C₅×C₈	—	2	2	no	—
78	C₂²×C₅×C₈	—	2	2	no	—
79	C₂²×C₅×C₈	—	2	2	no	—
80	C₂²×C₅×C₈	—	4	1	no	—
81	C₂²×C₅×C₈	—	4	1	no	—
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₅×D₄	—	2	2	no	—
91	C₄×C₅×D₄	—	2	2	no	—
92	C₄×C₅×D₄	—	2	2	no	—
93	C₄×C₅×D₄	—	2	2	no	—
94	C₄×C₅×D₄	—	2	2	no	—
95	C₄×C₅×D₄	—	2	2	no	—
96	C₅×#117	—	2	2	no	—
97	C₅×#117	—	2	2	no	—
98	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₈	—	2	2	no	—
122	C₅×C₄⋊C₈	—	2	2	no	—
123	C₅×C₄⋊C₈	—	2	2	no	—
124	C₅×C₄⋊C₈	—	2	2	no	—
125	C₅×C₄⋊C₈	—	2	2	no	—
126	C₅×C₄⋊C₈	D₄	1	4	yes	complemented
127	C₅×C₂²⋊C₈	—	2	2	no	—
128	C₅×C₂²⋊C₈	—	2	2	no	—
129	C₅×C₂²⋊C₈	—	2	2	no	—
130	C₅×C₂²⋊C₈	—	2	2	no	—
131	C₅×C₂²⋊C₈	—	2	2	no	—
132	C₅×C₂²⋊C₈	—	4	1	no	—
133	C₅×C₂²⋊C₈	—	4	1	no	—
134	C₅×C₂²⋊C₈	D₄	1	4	yes	complemented
135	C₅×#97	—	2	2	no	—
136	C₄×C₅×C₈	—	2	2	no	—
137	C₄×C₅×C₈	—	2	2	no	—
138	C₄×C₅×C₈	—	2	2	no	—
139	C₅×#95	C₂×C₄	1	1	yes	characteristic
140	C₅×#95	C₂×C₄	1	1	yes	characteristic
141	C₅×#95	C₂×C₄	1	1	yes	characteristic
142	C₅×#95	C₂×C₄	1	1	yes	characteristic
143	C₅×#95	C₂×C₄	1	1	yes	characteristic
144	C₅×#95	C₂×C₄	1	1	yes	characteristic
145	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×#435	C₂×C₅	1	1	yes	characteristic, complemented
147	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×#424	C₂×C₅	1	1	yes	characteristic, complemented
149	#2392	C₂×C₅	1	1	yes	characteristic
150	#1954	C₂×C₅	1	1	yes	characteristic, complemented
151	#1940	C₂×C₅	1	1	yes	characteristic, complemented
152	#1923	C₂×C₅	1	1	yes	characteristic, complemented
153	#1923	C₂×C₅	1	1	yes	characteristic, complemented
154	#1870	C₂×C₅	1	1	yes	characteristic, complemented
155	#1869	C₂×C₅	1	1	yes	characteristic, complemented
156	#1851	C₂×C₅	1	1	yes	characteristic, complemented
157	#1850	C₂×C₅	1	1	yes	characteristic, complemented
158	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
159	#1750	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
162	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×D₄	—	2	2	no	—
164	C₂×C₅×D₄	—	2	2	no	—
165	C₂×C₅×D₄	—	2	2	no	—
166	C₂×C₅×D₄	—	2	2	no	—
167	C₂×C₅×D₄	—	2	2	no	—
168	C₂×C₅×D₄	—	2	2	no	—
169	C₂×C₅×D₄	—	2	2	no	—
170	C₂×C₅×D₄	—	4	1	no	—
171	C₂×C₅×D₄	—	4	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₅	#41	1	2	yes	—
201	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
202	C₅×M₁₆	—	4	4	no	—
203	C₅×M₁₆	—	4	4	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	2	1	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	1	no	—
223	C₂×C₅×C₈	—	2	1	no	—
224	C₂×C₅×C₈	—	4	4	no	—
225	C₂×C₅×C₈	—	4	4	no	—
226	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
227	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
228	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
229	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
230	C₅×C₄⋊C₄	—	2	2	no	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	2	2	no	—
233	C₅×C₄⋊C₄	—	2	2	no	—
234	C₅×C₄⋊C₄	—	2	2	no	—
235	C₅×C₄⋊C₄	—	2	2	no	—
236	C₅×C₄⋊C₄	—	2	2	no	—
237	C₅×C₂²⋊C₄	—	2	2	no	—
238	C₅×C₂²⋊C₄	—	2	2	no	—
239	C₅×C₂²⋊C₄	—	2	2	no	—
240	C₅×C₂²⋊C₄	—	2	2	no	—
241	C₅×C₂²⋊C₄	—	2	2	no	—
242	C₅×C₂²⋊C₄	—	2	2	no	—
243	C₅×C₂²⋊C₄	—	2	2	no	—
244	C₅×C₂²⋊C₄	—	2	2	no	—
245	C₅×C₂²⋊C₄	—	2	2	no	—
246	C₅×C₂²⋊C₄	—	2	2	no	—
247	C₅×C₂²⋊C₄	—	2	2	no	—
248	C₅×C₂²⋊C₄	—	4	1	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	—	2	1	no	—
253	C₄²×C₅	—	2	1	no	—
254	C₄²×C₅	—	2	1	no	—
255	C₄²×C₅	C₂×D₄	1	2	yes	—
256	C₄²×C₅	#41	1	2	yes	—
257	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
258	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
259	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
260	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
264	C₂×#117	C₂²×C₅	1	1	yes	characteristic
265	#436	—	2	4	no	—
266	#435	—	2	4	no	—
267	C₈×D₄	—	2	4	no	—
268	#424	—	2	4	no	—
269	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	C₂×#97	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
287	#398	C₄×C₅	1	1	yes	characteristic
288	#397	C₄×C₅	1	1	yes	characteristic
289	#396	C₄×C₅	1	1	yes	characteristic
290	#396	C₄×C₅	1	1	yes	characteristic
291	#394	C₄×C₅	1	1	yes	characteristic
292	#394	C₄×C₅	1	1	yes	characteristic
293	#394	C₄×C₅	1	1	yes	characteristic
294	#392	C₄×C₅	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
296	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
297	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
298	#336	C₂²×C₅	1	1	yes	characteristic
299	#336	C₂²×C₅	1	1	yes	characteristic
300	#336	C₂²×C₅	1	1	yes	characteristic
301	#336	C₂²×C₅	1	1	yes	characteristic
302	#336	C₂²×C₅	1	1	yes	characteristic
303	#336	C₂²×C₅	1	1	yes	characteristic
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	2	1	no	—
307	C₂³×C₅	—	2	1	no	—
308	C₂³×C₅	—	2	1	no	—
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	—	2	1	no	—
311	C₂³×C₅	—	2	1	no	—
312	C₂³×C₅	—	2	1	no	—
313	C₂³×C₅	—	2	1	no	—
314	C₂³×C₅	—	2	1	no	—
315	C₂³×C₅	—	2	1	no	—
316	C₂³×C₅	—	2	1	no	—
317	C₂³×C₅	—	2	1	no	—
318	C₂³×C₅	—	2	1	no	—
319	C₂³×C₅	—	2	1	no	—
320	C₂³×C₅	—	2	1	no	—
321	C₂³×C₅	—	2	1	no	—
322	C₂³×C₅	—	2	1	no	—
323	C₂³×C₅	C₄×D₄	1	2	yes	—
324	C₂³×C₅	#131	1	2	yes	—
325	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
326	C₅×D₄	—	2	8	no	—
327	C₅×D₄	—	4	4	no	—
328	C₅×D₄	—	4	4	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	1	no	—
360	C₂×C₄×C₅	—	2	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	—	4	1	no	—
363	C₂×C₄×C₅	—	4	1	no	—
364	C₂×C₄×C₅	—	4	1	no	—
365	C₂×C₄×C₅	—	4	1	no	—
366	C₂×C₄×C₅	—	4	1	no	—
367	C₂×C₄×C₅	—	4	1	no	—
368	C₂×C₄×C₅	—	4	1	no	—
369	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
370	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
371	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
372	C₂×C₄×C₅	#131	1	2	yes	—
373	C₂×C₄×C₅	#131	1	2	yes	—
374	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
377	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
378	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
380	C₅×C₈	—	2	2	no	—
381	C₅×C₈	—	2	2	no	—
382	C₅×C₈	—	2	2	no	—
383	C₅×C₈	—	2	2	no	—
384	C₅×C₈	—	4	1	no	—
385	C₅×C₈	—	4	1	no	—
386	C₅×C₈	—	4	1	no	—
387	C₅×C₈	—	4	1	no	—
388	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
389	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
390	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	2	2	no	—
397	C₂×M₁₆	—	2	2	no	—
398	C₂×M₁₆	—	4	1	no	—
399	C₂×M₁₆	—	4	1	no	—
400	C₂²×C₈	—	2	2	no	—
401	C₂²×C₈	—	2	2	no	—
402	C₂²×C₈	—	2	2	no	—
403	C₂²×C₈	—	2	2	no	—
404	C₂²×C₈	—	4	1	no	—
405	C₂²×C₈	—	4	1	no	—
406	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	#117	—	2	2	no	—
421	#117	—	2	2	no	—
422	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
445	C₄⋊C₈	—	2	2	no	—
446	C₄⋊C₈	—	2	2	no	—
447	C₄⋊C₈	—	2	2	no	—
448	C₄⋊C₈	—	2	2	no	—
449	C₄⋊C₈	—	2	2	no	—
450	C₄⋊C₈	C₅×D₄	1	4	yes	complemented
451	C₂²⋊C₈	—	2	2	no	—
452	C₂²⋊C₈	—	2	2	no	—
453	C₂²⋊C₈	—	2	2	no	—
454	C₂²⋊C₈	—	2	2	no	—
455	C₂²⋊C₈	—	2	2	no	—
456	C₂²⋊C₈	—	4	1	no	—
457	C₂²⋊C₈	—	4	1	no	—
458	C₂²⋊C₈	C₅×D₄	1	4	yes	complemented
459	#97	—	2	2	no	—
460	C₄×C₈	—	2	2	no	—
461	C₄×C₈	—	2	2	no	—
462	C₄×C₈	—	2	2	no	—
463	#95	C₂×C₄×C₅	1	1	yes	characteristic
464	#95	C₂×C₄×C₅	1	1	yes	characteristic
465	#95	C₂×C₄×C₅	1	1	yes	characteristic
466	#95	C₂×C₄×C₅	1	1	yes	characteristic
467	#95	C₂×C₄×C₅	1	1	yes	characteristic
468	#95	C₂×C₄×C₅	1	1	yes	characteristic
469	C₂²×C₅	—	2	2	no	—
470	C₂²×C₅	—	2	2	no	—
471	C₂²×C₅	—	2	2	no	—
472	C₂²×C₅	—	2	2	no	—
473	C₂²×C₅	—	2	2	no	—
474	C₂²×C₅	—	2	2	no	—
475	C₂²×C₅	—	4	1	no	—
476	C₂²×C₅	—	4	1	no	—
477	C₂²×C₅	—	4	1	no	—
478	C₂²×C₅	—	4	1	no	—
479	C₂²×C₅	—	4	1	no	—
480	C₂²×C₅	—	4	1	no	—
481	C₂²×C₅	—	4	1	no	—
482	C₂²×C₅	—	4	1	no	—
483	C₂²×C₅	—	4	1	no	—
484	C₂²×C₅	—	4	1	no	—
485	C₂²×C₅	—	4	1	no	—
486	C₂²×C₅	—	4	1	no	—
487	C₂²×C₅	—	4	1	no	—
488	C₂²×C₅	—	4	1	no	—
489	C₂²×C₅	—	4	1	no	—
490	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
491	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
492	C₂²×C₅	#520	1	1	yes	characteristic
493	C₂²×C₅	C₂×#131	1	1	yes	characteristic
494	C₂²×C₅	C₂×#131	1	1	yes	characteristic
495	C₂²×C₅	C₂×#131	1	1	yes	characteristic
496	C₂²×C₅	#568	1	1	yes	characteristic
497	C₄×C₅	—	2	2	no	—
498	C₄×C₅	—	2	2	no	—
499	C₄×C₅	—	2	2	no	—
500	C₄×C₅	—	2	2	no	—
501	C₄×C₅	—	2	2	no	—
502	C₄×C₅	—	4	1	no	—
503	C₄×C₅	—	4	1	no	—
504	C₄×C₅	—	4	1	no	—
505	C₄×C₅	—	4	1	no	—
506	C₄×C₅	—	4	1	no	—
507	C₄×C₅	—	4	1	no	—
508	C₄×C₅	D₄²	1	1	yes	characteristic
509	C₄×C₅	#547	1	1	yes	characteristic
510	C₄×C₅	#548	1	1	yes	characteristic
511	C₄×C₅	#553	1	1	yes	characteristic
512	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
513	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
514	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	4	1	no	—
523	C₂×D₄	—	4	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
549	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
550	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
551	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
552	C₂²×C₄	C₅×#41	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
554	M₁₆	—	4	4	no	—
555	M₁₆	—	4	4	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	4	4	no	—
577	C₂×C₈	—	4	4	no	—
578	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
579	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
580	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
581	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	C₂×C₅×D₄	1	2	yes	—
608	C₄²	C₅×#41	1	2	yes	—
609	C₂×C₅	—	4	2	no	—
610	C₂×C₅	—	4	2	no	—
611	C₂×C₅	—	8	1	no	—
612	C₂×C₅	#2361	1	1	yes	characteristic
613	C₂×C₅	#2929	1	1	yes	characteristic
614	C₂×C₅	#2931	1	1	yes	characteristic
615	C₂×C₅	#2933	1	1	yes	characteristic
616	C₂×C₅	#2933	1	1	yes	characteristic
617	C₂×C₅	#2993	1	1	yes	characteristic
618	C₂×C₅	#2994	1	1	yes	characteristic
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	C₄×C₅×D₄	1	2	yes	—
639	C₂³	C₅×#131	1	2	yes	—
640	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
641	D₄	—	2	8	no	—
642	D₄	—	4	4	no	—
643	D₄	—	4	4	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
685	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
686	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
687	C₂×C₄	C₅×#131	1	2	yes	—
688	C₂×C₄	C₅×#131	1	2	yes	—
689	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
690	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
691	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
692	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
693	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
695	C₈	—	2	2	no	—
696	C₈	—	2	2	no	—
697	C₈	—	2	2	no	—
698	C₈	—	2	2	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	1	no	—
703	C₅	#22992	1	1	yes	characteristic, direct product factor, Sylow
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
726	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
727	C₂²	C₅×#520	1	1	yes	characteristic
728	C₂²	C₂×C₅×#131	1	1	yes	characteristic
729	C₂²	C₂×C₅×#131	1	1	yes	characteristic
730	C₂²	C₂×C₅×#131	1	1	yes	characteristic
731	C₂²	C₅×#568	1	1	yes	characteristic
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	2	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	C₅×D₄²	1	1	yes	characteristic
744	C₄	C₅×#547	1	1	yes	characteristic
745	C₄	C₅×#548	1	1	yes	characteristic
746	C₄	C₅×#553	1	1	yes	characteristic
747	C₂	—	4	2	no	—
748	C₂	—	4	2	no	—
749	C₂	—	8	1	no	—
750	C₂	C₅×#2361	1	1	yes	characteristic
751	C₂	C₅×#2929	1	1	yes	characteristic
752	C₂	C₅×#2931	1	1	yes	characteristic
753	C₂	C₅×#2933	1	1	yes	characteristic
754	C₂	C₅×#2933	1	1	yes	characteristic
755	C₂	C₅×#2993	1	1	yes	characteristic
756	C₂	C₅×#2994	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₅×#392	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#436	C₂	semidirect
2. C₂×C₅×#435	C₂	semidirect
3. C₂×C₅×C₈×D₄	C₂	semidirect
4. C₂×C₅×#424	C₂	semidirect
6. C₅×#1954	C₂	semidirect
7. C₅×#1940	C₂	semidirect
8. C₅×#1923	C₂	semidirect
9. C₅×#1923	C₂	semidirect
10. C₅×#1870	C₂	semidirect
11. C₅×#1869	C₂	semidirect
12. C₅×#1851	C₂	semidirect
13. C₅×#1850	C₂	semidirect
14. C₅×C₈×C₄⋊C₄	C₂	semidirect
15. C₅×#1750	C₂	semidirect
63. #22992	C₅	direct (N × H)
126. C₅×C₄⋊C₈	D₄	semidirect
134. C₅×C₂²⋊C₈	D₄	semidirect
145. C₂×#436	C₂×C₅	semidirect
146. C₂×#435	C₂×C₅	semidirect
147. C₂×C₈×D₄	C₂×C₅	semidirect
148. C₂×#424	C₂×C₅	semidirect
150. #1954	C₂×C₅	semidirect
151. #1940	C₂×C₅	semidirect
152. #1923	C₂×C₅	semidirect
153. #1923	C₂×C₅	semidirect
154. #1870	C₂×C₅	semidirect
155. #1869	C₂×C₅	semidirect
156. #1851	C₂×C₅	semidirect
157. #1850	C₂×C₅	semidirect
158. C₈×C₄⋊C₄	C₂×C₅	semidirect
159. #1750	C₂×C₅	semidirect
450. C₄⋊C₈	C₅×D₄	semidirect
458. C₂²⋊C₈	C₅×D₄	semidirect
703. C₅	#22992	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×C₅×#436	2
C₂×C₅×#435	2
C₂×C₅×C₈×D₄	2
C₂×C₅×#424	2
C₅×#2392	2
C₅×#1954	2
C₅×#1940	2
C₅×#1923	2
C₅×#1870	2
C₅×#1869	2
C₅×#1851	2
C₅×#1850	2
C₅×C₈×C₄⋊C₄	2
C₅×#1750	2
#22992	5

Subgroups — C5×#22992 #11945712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22992 #11945712