Subgroups — C₅×#23085 #11945805

Order 1280.

978 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic
4	C₅×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1955	C₂	1	1	yes	maximal, characteristic, complemented
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×#1771	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1753	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1749	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#121	C₄	1	1	yes	characteristic
19	C₂×C₄×C₅×D₄	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	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₅×#435	—	2	4	no	—
24	C₅×#431	—	2	4	no	—
25	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₂²⋊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×#97	C₂²	1	1	yes	characteristic
40	C₂×C₅×#97	C₂²	1	1	yes	characteristic
41	C₂×C₅×#97	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×C₈	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	C₅×#390	C₄	1	1	yes	characteristic
46	C₅×#389	C₄	1	1	yes	characteristic
47	C₅×#388	C₄	1	1	yes	characteristic
48	C₅×#388	C₄	1	1	yes	characteristic
49	C₅×#386	C₄	1	1	yes	characteristic
50	C₅×#386	C₄	1	1	yes	characteristic
51	C₅×#380	C₄	1	1	yes	characteristic
52	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₅×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	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	#23085	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₅	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	—	4	1	no	—
73	C₂²×C₅×C₈	—	2	2	no	—
74	C₂²×C₅×C₈	—	2	2	no	—
75	C₂²×C₅×C₈	—	4	1	no	—
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₅×#121	—	2	4	no	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₄×C₅×D₄	—	4	1	no	—
88	C₄×C₅×D₄	—	4	1	no	—
89	C₄×C₅×D₄	—	4	1	no	—
90	C₄×C₅×D₄	—	4	1	no	—
91	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₅	—	2	2	no	—
107	C₂×C₄²×C₅	—	2	2	no	—
108	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×C₄⋊C₈	—	2	2	no	—
115	C₅×C₄⋊C₈	—	4	1	no	—
116	C₅×C₄⋊C₈	—	4	1	no	—
117	C₅×C₄⋊C₈	D₄	1	4	yes	complemented
118	C₅×C₂²⋊C₈	—	2	2	no	—
119	C₅×C₂²⋊C₈	—	2	2	no	—
120	C₅×C₂²⋊C₈	—	2	2	no	—
121	C₅×C₂²⋊C₈	—	2	2	no	—
122	C₅×C₂²⋊C₈	—	2	2	no	—
123	C₅×C₂²⋊C₈	—	2	2	no	—
124	C₅×C₂²⋊C₈	—	2	2	no	—
125	C₅×C₂²⋊C₈	—	2	2	no	—
126	C₅×C₂²⋊C₈	—	4	1	no	—
127	C₅×C₂²⋊C₈	—	4	1	no	—
128	C₅×#97	—	2	2	no	—
129	C₅×#97	—	2	2	no	—
130	C₅×#97	—	4	1	no	—
131	C₄×C₅×C₈	—	2	2	no	—
132	C₄×C₅×C₈	—	2	2	no	—
133	C₄×C₅×C₈	—	4	1	no	—
134	C₅×#95	C₂×C₄	1	1	yes	characteristic
135	C₅×#95	C₂×C₄	1	1	yes	characteristic
136	C₅×#95	C₂×C₄	1	1	yes	characteristic
137	C₅×#95	C₂×C₄	1	1	yes	characteristic
138	C₅×#95	C₂×C₄	1	1	yes	characteristic
139	C₅×#95	C₂×C₄	1	1	yes	characteristic
140	C₂×#435	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#431	C₂×C₅	1	1	yes	characteristic, complemented
142	C₄×#121	C₂×C₅	1	1	yes	characteristic
143	#1955	C₂×C₅	1	1	yes	characteristic, complemented
144	#1955	C₂×C₅	1	1	yes	characteristic, complemented
145	#1954	C₂×C₅	1	1	yes	characteristic, complemented
146	#1940	C₂×C₅	1	1	yes	characteristic, complemented
147	#1923	C₂×C₅	1	1	yes	characteristic, complemented
148	#1923	C₂×C₅	1	1	yes	characteristic, complemented
149	#1870	C₂×C₅	1	1	yes	characteristic, complemented
150	#1869	C₂×C₅	1	1	yes	characteristic, complemented
151	#1771	C₂×C₅	1	1	yes	characteristic, complemented
152	#1753	C₂×C₅	1	1	yes	characteristic, complemented
153	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
154	#1749	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	—	2	2	no	—
160	C₂×C₅×D₄	—	2	2	no	—
161	C₂×C₅×D₄	—	2	2	no	—
162	C₂×C₅×D₄	—	2	2	no	—
163	C₂×C₅×D₄	—	2	2	no	—
164	C₂×C₅×D₄	—	4	1	no	—
165	C₂×C₅×D₄	—	4	1	no	—
166	C₂×C₅×D₄	—	4	1	no	—
167	C₂²×C₄×C₅	—	2	2	no	—
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	—	2	2	no	—
170	C₂²×C₄×C₅	—	2	2	no	—
171	C₂²×C₄×C₅	—	2	2	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	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	4	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
226	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
227	C₂×C₅×C₈	#41	1	2	yes	—
228	C₂×C₅×C₈	#41	1	2	yes	—
229	C₅×C₄⋊C₄	—	2	2	no	—
230	C₅×C₄⋊C₄	—	2	2	no	—
231	C₅×C₄⋊C₄	—	4	1	no	—
232	C₅×C₄⋊C₄	—	4	1	no	—
233	C₅×C₄⋊C₄	—	4	1	no	—
234	C₅×C₂²⋊C₄	—	2	2	no	—
235	C₅×C₂²⋊C₄	—	2	2	no	—
236	C₅×C₂²⋊C₄	—	2	2	no	—
237	C₅×C₂²⋊C₄	—	2	2	no	—
238	C₅×C₂²⋊C₄	—	2	2	no	—
239	C₅×C₂²⋊C₄	—	4	1	no	—
240	C₅×C₂²⋊C₄	—	4	1	no	—
241	C₅×C₂²⋊C₄	—	4	1	no	—
242	C₅×C₂²⋊C₄	—	4	1	no	—
243	C₅×C₂²⋊C₄	M₁₆	1	4	yes	complemented
244	C₄²×C₅	—	2	2	no	—
245	C₄²×C₅	—	2	2	no	—
246	C₄²×C₅	—	2	1	no	—
247	C₄²×C₅	—	2	1	no	—
248	C₄²×C₅	—	2	1	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	C₂×D₄	1	2	yes	—
253	C₄²×C₅	#41	1	2	yes	—
254	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
255	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
256	C₂×#121	C₄×C₅	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
260	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
261	#435	—	2	4	no	—
262	#431	—	2	4	no	—
263	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₂²⋊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×#97	C₂²×C₅	1	1	yes	characteristic
278	C₂×#97	C₂²×C₅	1	1	yes	characteristic
279	C₂×#97	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
283	#390	C₄×C₅	1	1	yes	characteristic
284	#389	C₄×C₅	1	1	yes	characteristic
285	#388	C₄×C₅	1	1	yes	characteristic
286	#388	C₄×C₅	1	1	yes	characteristic
287	#386	C₄×C₅	1	1	yes	characteristic
288	#386	C₄×C₅	1	1	yes	characteristic
289	#380	C₄×C₅	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
293	#336	C₂²×C₅	1	1	yes	characteristic
294	#336	C₂²×C₅	1	1	yes	characteristic
295	#336	C₂²×C₅	1	1	yes	characteristic
296	#336	C₂²×C₅	1	1	yes	characteristic
297	#336	C₂²×C₅	1	1	yes	characteristic
298	#336	C₂²×C₅	1	1	yes	characteristic
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	—	2	1	no	—
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	—	2	1	no	—
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	C₂×M₁₆	1	2	yes	—
319	C₂³×C₅	#131	1	2	yes	—
320	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
321	C₅×D₄	—	4	4	no	—
322	C₅×D₄	—	4	4	no	—
323	C₅×D₄	—	4	4	no	—
324	C₂×C₄×C₅	—	2	8	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	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	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	1	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	—	4	4	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	—	4	1	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	4	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	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	C₄×D₄	1	2	yes	—
367	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
368	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
369	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
370	C₂×C₄×C₅	#131	1	2	yes	—
371	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
373	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
374	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
375	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
377	C₅×C₈	—	2	2	no	—
378	C₅×C₈	—	2	2	no	—
379	C₅×C₈	—	2	2	no	—
380	C₅×C₈	—	2	2	no	—
381	C₅×C₈	—	4	1	no	—
382	C₅×C₈	—	4	1	no	—
383	C₅×C₈	—	4	1	no	—
384	C₅×C₈	—	4	1	no	—
385	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
386	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
387	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
388	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
389	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
393	C₂×M₁₆	—	2	2	no	—
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	—	4	1	no	—
396	C₂²×C₈	—	2	2	no	—
397	C₂²×C₈	—	2	2	no	—
398	C₂²×C₈	—	4	1	no	—
399	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
407	#121	—	2	4	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	4	1	no	—
411	C₄×D₄	—	4	1	no	—
412	C₄×D₄	—	4	1	no	—
413	C₄×D₄	—	4	1	no	—
414	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
429	C₂×C₄²	—	2	2	no	—
430	C₂×C₄²	—	2	2	no	—
431	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
432	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
437	C₄⋊C₈	—	2	2	no	—
438	C₄⋊C₈	—	4	1	no	—
439	C₄⋊C₈	—	4	1	no	—
440	C₄⋊C₈	C₅×D₄	1	4	yes	complemented
441	C₂²⋊C₈	—	2	2	no	—
442	C₂²⋊C₈	—	2	2	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	C₂²⋊C₈	—	2	2	no	—
445	C₂²⋊C₈	—	2	2	no	—
446	C₂²⋊C₈	—	2	2	no	—
447	C₂²⋊C₈	—	2	2	no	—
448	C₂²⋊C₈	—	2	2	no	—
449	C₂²⋊C₈	—	4	1	no	—
450	C₂²⋊C₈	—	4	1	no	—
451	#97	—	2	2	no	—
452	#97	—	2	2	no	—
453	#97	—	4	1	no	—
454	C₄×C₈	—	2	2	no	—
455	C₄×C₈	—	2	2	no	—
456	C₄×C₈	—	4	1	no	—
457	#95	C₂×C₄×C₅	1	1	yes	characteristic
458	#95	C₂×C₄×C₅	1	1	yes	characteristic
459	#95	C₂×C₄×C₅	1	1	yes	characteristic
460	#95	C₂×C₄×C₅	1	1	yes	characteristic
461	#95	C₂×C₄×C₅	1	1	yes	characteristic
462	#95	C₂×C₄×C₅	1	1	yes	characteristic
463	C₂²×C₅	—	2	2	no	—
464	C₂²×C₅	—	2	2	no	—
465	C₂²×C₅	—	2	2	no	—
466	C₂²×C₅	—	2	2	no	—
467	C₂²×C₅	—	2	2	no	—
468	C₂²×C₅	—	2	2	no	—
469	C₂²×C₅	—	4	1	no	—
470	C₂²×C₅	—	4	1	no	—
471	C₂²×C₅	—	4	1	no	—
472	C₂²×C₅	—	4	1	no	—
473	C₂²×C₅	—	4	1	no	—
474	C₂²×C₅	—	4	1	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	C₂×C₄×D₄	1	1	yes	characteristic
485	C₂²×C₅	C₄×#41	1	1	yes	characteristic
486	C₂²×C₅	#518	1	1	yes	characteristic
487	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
488	C₂²×C₅	C₂×#131	1	1	yes	characteristic
489	C₂²×C₅	C₂×#131	1	1	yes	characteristic
490	C₂²×C₅	#568	1	1	yes	characteristic
491	C₄×C₅	—	2	2	no	—
492	C₄×C₅	—	2	2	no	—
493	C₄×C₅	—	2	2	no	—
494	C₄×C₅	—	2	2	no	—
495	C₄×C₅	—	2	2	no	—
496	C₄×C₅	—	4	1	no	—
497	C₄×C₅	—	4	1	no	—
498	C₄×C₅	—	4	1	no	—
499	C₄×C₅	—	4	1	no	—
500	C₄×C₅	—	4	1	no	—
501	C₄×C₅	—	4	1	no	—
502	C₄×C₅	#546	1	1	yes	characteristic
503	C₄×C₅	#550	1	1	yes	characteristic
504	C₄×C₅	#553	1	1	yes	characteristic
505	C₄×C₅	#555	1	1	yes	characteristic
506	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
507	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
508	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	4	1	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	—	4	1	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	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	—	2	1	no	—
541	C₂²×C₄	—	4	1	no	—
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	C₂²×C₄×C₅	1	1	yes	characteristic
552	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
554	M₁₆	—	4	4	no	—
555	C₂×C₈	—	2	1	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	—	4	4	no	—
576	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
577	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
578	C₂×C₈	C₅×#41	1	2	yes	—
579	C₂×C₈	C₅×#41	1	2	yes	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	4	1	no	—
583	C₄⋊C₄	—	4	1	no	—
584	C₄⋊C₄	—	4	1	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₂²⋊C₄	—	4	1	no	—
594	C₂²⋊C₄	C₅×M₁₆	1	4	yes	complemented
595	C₄²	—	2	2	no	—
596	C₄²	—	2	2	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	C₂×C₅×D₄	1	2	yes	—
604	C₄²	C₅×#41	1	2	yes	—
605	C₂×C₅	—	4	2	no	—
606	C₂×C₅	—	4	2	no	—
607	C₂×C₅	—	8	1	no	—
608	C₂×C₅	#2363	1	1	yes	characteristic
609	C₂×C₅	#2929	1	1	yes	characteristic
610	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
611	C₂×C₅	#2965	1	1	yes	characteristic
612	C₂×C₅	#2968	1	1	yes	characteristic
613	C₂×C₅	#2974	1	1	yes	characteristic
614	C₂×C₅	#2981	1	1	yes	characteristic
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
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	C₂×C₅×M₁₆	1	2	yes	—
635	C₂³	C₅×#131	1	2	yes	—
636	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
637	D₄	—	4	4	no	—
638	D₄	—	4	4	no	—
639	D₄	—	4	4	no	—
640	C₂×C₄	—	2	8	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	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	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	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	—	4	4	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	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	C₄×C₅×D₄	1	2	yes	—
683	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
684	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
685	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
686	C₂×C₄	C₅×#131	1	2	yes	—
687	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
688	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
689	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
690	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
691	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
692	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
693	C₈	—	2	2	no	—
694	C₈	—	2	2	no	—
695	C₈	—	2	2	no	—
696	C₈	—	2	2	no	—
697	C₈	—	4	1	no	—
698	C₈	—	4	1	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₅	#23085	1	1	yes	characteristic, direct product factor, Sylow
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	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	C₂×C₄×C₅×D₄	1	1	yes	characteristic
724	C₂²	C₄×C₅×#41	1	1	yes	characteristic
725	C₂²	C₅×#518	1	1	yes	characteristic
726	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
727	C₂²	C₂×C₅×#131	1	1	yes	characteristic
728	C₂²	C₂×C₅×#131	1	1	yes	characteristic
729	C₂²	C₅×#568	1	1	yes	characteristic
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	2	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	C₅×#546	1	1	yes	characteristic
742	C₄	C₅×#550	1	1	yes	characteristic
743	C₄	C₅×#553	1	1	yes	characteristic
744	C₄	C₅×#555	1	1	yes	characteristic
745	C₂	—	4	2	no	—
746	C₂	—	4	2	no	—
747	C₂	—	8	1	no	—
748	C₂	C₅×#2363	1	1	yes	characteristic
749	C₂	C₅×#2929	1	1	yes	characteristic
750	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
751	C₂	C₅×#2965	1	1	yes	characteristic
752	C₂	C₅×#2968	1	1	yes	characteristic
753	C₂	C₅×#2974	1	1	yes	characteristic
754	C₂	C₅×#2981	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	C₂×C₅×#121	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×#435	C₂	semidirect
2. C₂×C₅×#431	C₂	semidirect
4. C₅×#1955	C₂	semidirect
5. C₅×#1955	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×#1771	C₂	semidirect
13. C₅×#1753	C₂	semidirect
14. C₅×C₈×C₂²⋊C₄	C₂	semidirect
15. C₅×#1749	C₂	semidirect
61. #23085	C₅	direct (N × H)
117. C₅×C₄⋊C₈	D₄	semidirect
140. C₂×#435	C₂×C₅	semidirect
141. C₂×#431	C₂×C₅	semidirect
143. #1955	C₂×C₅	semidirect
144. #1955	C₂×C₅	semidirect
145. #1954	C₂×C₅	semidirect
146. #1940	C₂×C₅	semidirect
147. #1923	C₂×C₅	semidirect
148. #1923	C₂×C₅	semidirect
149. #1870	C₂×C₅	semidirect
150. #1869	C₂×C₅	semidirect
151. #1771	C₂×C₅	semidirect
152. #1753	C₂×C₅	semidirect
153. C₈×C₂²⋊C₄	C₂×C₅	semidirect
154. #1749	C₂×C₅	semidirect
243. C₅×C₂²⋊C₄	M₁₆	semidirect
440. C₄⋊C₈	C₅×D₄	semidirect
594. C₂²⋊C₄	C₅×M₁₆	semidirect
701. C₅	#23085	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×#435	2
C₂×C₅×#431	2
C₄×C₅×#121	2
C₅×#1955	2
C₅×#1954	2
C₅×#1940	2
C₅×#1923	2
C₅×#1870	2
C₅×#1869	2
C₅×#1771	2
C₅×#1753	2
C₅×C₈×C₂²⋊C₄	2
C₅×#1749	2
#23085	5

Subgroups — C5×#23085 #11945805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23085 #11945805