Subgroups — C₅×#22056 #11944776

Order 1280.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#447	C₂	1	1	yes	maximal, characteristic
2	C₅×#2324	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1972	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1934	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1875	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂×C₅×#117	C₂²	1	1	yes	characteristic
23	C₅×#447	C₄	1	8	yes	complemented
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#102	C₂²	1	1	yes	characteristic
27	C₂×C₅×#102	C₂²	1	1	yes	characteristic
28	C₂×C₅×#102	C₂²	1	1	yes	characteristic
29	C₂×C₅×#102	C₂²	1	1	yes	characteristic
30	C₂×C₅×#102	C₂²	1	1	yes	characteristic
31	C₂×C₅×#102	C₂²	1	1	yes	characteristic
32	C₂×C₅×#102	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#102	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
38	C₅×#390	—	2	1	no	—
39	C₅×#390	—	2	1	no	—
40	C₅×#390	—	2	1	no	—
41	C₅×#390	C₂²	1	1	yes	characteristic
42	C₅×#390	C₂²	1	1	yes	characteristic
43	C₅×#390	C₂²	1	1	yes	characteristic
44	C₅×#390	C₂²	1	1	yes	characteristic
45	C₅×#390	C₂²	1	1	yes	characteristic, complemented
46	C₅×#389	C₂²	1	1	yes	characteristic, complemented
47	C₅×#388	—	2	1	no	—
48	C₅×#386	—	2	1	no	—
49	C₅×#385	—	2	1	no	—
50	C₅×#380	C₂²	1	1	yes	characteristic
51	C₅×#379	—	2	1	no	—
52	C₅×#379	—	2	1	no	—
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₅×#340	C₂²	1	1	yes	characteristic, complemented
55	C₅×#340	C₂²	1	1	yes	characteristic, complemented
56	C₅×#340	C₂²	1	1	yes	characteristic, complemented
57	C₅×#340	C₂²	1	1	yes	characteristic, complemented
58	C₅×#336	C₂²	1	1	yes	characteristic, complemented
59	C₅×#336	C₂²	1	1	yes	characteristic, complemented
60	#22056	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁵×C₅	—	2	1	no	—
62	C₂²×C₅×D₄	—	2	1	no	—
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	—	2	2	no	—
65	C₂²×C₅×D₄	—	4	1	no	—
66	C₂²×C₅×D₄	—	4	1	no	—
67	C₂²×C₅×D₄	—	4	1	no	—
68	C₂²×C₅×D₄	—	4	1	no	—
69	C₂²×C₅×D₄	C₂×C₄	1	4	yes	complemented
70	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅	—	2	1	no	—
74	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₅×D₈	—	4	1	no	—
76	C₂×C₅×D₈	—	4	1	no	—
77	C₂×C₅×D₈	—	4	1	no	—
78	C₂×C₅×D₈	—	4	1	no	—
79	C₂×C₅×D₈	C₂×C₄	1	4	yes	—
80	C₂×C₅×D₈	C₂×C₄	1	4	yes	—
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₅×#121	—	2	2	no	—
86	C₅×#121	C₂×C₄	1	4	yes	—
87	C₄×C₅×D₄	—	4	1	no	—
88	C₄×C₅×D₄	—	4	1	no	—
89	C₅×#117	—	4	1	no	—
90	C₅×#117	—	4	1	no	—
91	C₅×#117	—	4	1	no	—
92	C₅×#117	—	4	1	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₅	—	2	1	no	—
118	C₂×C₄²×C₅	—	2	1	no	—
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₅×#107	—	4	1	no	—
122	C₅×#106	—	4	1	no	—
123	C₅×#102	—	4	1	no	—
124	C₅×#102	—	4	1	no	—
125	C₅×#102	—	4	1	no	—
126	C₅×#102	—	4	1	no	—
127	C₅×#102	—	4	1	no	—
128	C₅×#102	—	4	1	no	—
129	C₅×#102	C₂×C₄	1	4	yes	complemented
130	C₅×#102	C₂×C₄	1	4	yes	complemented
131	C₅×C₂²⋊C₈	—	2	2	no	—
132	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
133	C₅×#97	—	4	1	no	—
134	C₄×C₅×C₈	—	4	1	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	—	2	1	no	—
137	C₅×#95	—	2	1	no	—
138	C₂×#447	C₂×C₅	1	1	yes	characteristic
139	#2324	C₂×C₅	1	1	yes	characteristic, complemented
140	#2309	C₂×C₅	1	1	yes	characteristic, complemented
141	#1972	C₂×C₅	1	1	yes	characteristic, complemented
142	#1970	C₂×C₅	1	1	yes	characteristic, complemented
143	#1936	C₂×C₅	1	1	yes	characteristic, complemented
144	#1934	C₂×C₅	1	1	yes	characteristic, complemented
145	#1926	C₂×C₅	1	1	yes	characteristic, complemented
146	#1925	C₂×C₅	1	1	yes	characteristic, complemented
147	#1879	C₂×C₅	1	1	yes	characteristic, complemented
148	#1879	C₂×C₅	1	1	yes	characteristic, complemented
149	#1875	C₂×C₅	1	1	yes	characteristic, complemented
150	#1854	C₂×C₅	1	1	yes	characteristic, complemented
151	#1786	C₂×C₅	1	1	yes	characteristic, complemented
152	#1750	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂⁴×C₅	—	2	1	no	—
154	C₂⁴×C₅	—	2	1	no	—
155	C₂⁴×C₅	—	2	1	no	—
156	C₂⁴×C₅	—	2	4	no	—
157	C₂⁴×C₅	—	4	2	no	—
158	C₂⁴×C₅	—	4	2	no	—
159	C₂⁴×C₅	—	8	1	no	—
160	C₂⁴×C₅	—	8	1	no	—
161	C₂⁴×C₅	—	8	1	no	—
162	C₂⁴×C₅	—	8	1	no	—
163	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂×C₅×D₄	—	2	4	no	—
165	C₂×C₅×D₄	—	2	4	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	2	1	no	—
177	C₂×C₅×D₄	—	2	1	no	—
178	C₂×C₅×D₄	—	2	1	no	—
179	C₂×C₅×D₄	—	2	1	no	—
180	C₂×C₅×D₄	—	2	1	no	—
181	C₂×C₅×D₄	—	4	4	no	—
182	C₂×C₅×D₄	—	4	4	no	—
183	C₂×C₅×D₄	—	4	2	no	—
184	C₂×C₅×D₄	—	4	2	no	—
185	C₂×C₅×D₄	—	4	4	no	—
186	C₂×C₅×D₄	—	4	4	no	—
187	C₂×C₅×D₄	—	8	1	no	—
188	C₂×C₅×D₄	—	8	1	no	—
189	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
190	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
191	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	—	2	1	no	—
201	C₂²×C₄×C₅	—	4	2	no	—
202	C₂²×C₄×C₅	—	8	1	no	—
203	C₂²×C₄×C₅	—	8	1	no	—
204	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
205	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₅	#41	1	2	yes	—
211	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
212	C₅×D₈	—	4	4	no	—
213	C₅×D₈	—	4	4	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	C₂²×C₄	1	2	yes	—
225	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	—	2	1	no	—
229	C₅×C₄⋊C₄	—	2	1	no	—
230	C₅×C₄⋊C₄	—	2	1	no	—
231	C₅×C₄⋊C₄	—	2	1	no	—
232	C₅×C₄⋊C₄	—	2	1	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	4	1	no	—
236	C₅×C₄⋊C₄	—	4	1	no	—
237	C₅×C₄⋊C₄	—	8	1	no	—
238	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
239	C₅×C₂²⋊C₄	—	2	4	no	—
240	C₅×C₂²⋊C₄	—	4	1	no	—
241	C₅×C₂²⋊C₄	—	4	1	no	—
242	C₅×C₂²⋊C₄	—	4	2	no	—
243	C₅×C₂²⋊C₄	—	4	2	no	—
244	C₅×C₂²⋊C₄	—	8	1	no	—
245	C₅×C₂²⋊C₄	—	8	1	no	—
246	C₅×C₂²⋊C₄	—	8	1	no	—
247	C₅×C₂²⋊C₄	—	8	1	no	—
248	C₅×C₂²⋊C₄	—	8	1	no	—
249	C₅×C₂²⋊C₄	—	8	1	no	—
250	C₅×C₂²⋊C₄	—	8	1	no	—
251	C₅×C₂²⋊C₄	—	8	1	no	—
252	C₅×C₂²⋊C₄	—	8	1	no	—
253	C₅×C₂²⋊C₄	—	8	1	no	—
254	C₅×C₂²⋊C₄	—	8	1	no	—
255	C₄²×C₅	—	2	1	no	—
256	C₄²×C₅	—	2	1	no	—
257	C₄²×C₅	—	2	1	no	—
258	C₄²×C₅	—	2	1	no	—
259	C₄²×C₅	—	4	2	no	—
260	C₄²×C₅	—	8	1	no	—
261	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
262	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
263	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×#121	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₂×#117	C₂²×C₅	1	1	yes	characteristic
267	C₂×#117	C₂²×C₅	1	1	yes	characteristic
268	#447	C₄×C₅	1	8	yes	complemented
269	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×#106	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×#102	C₂²×C₅	1	1	yes	characteristic
272	C₂×#102	C₂²×C₅	1	1	yes	characteristic
273	C₂×#102	C₂²×C₅	1	1	yes	characteristic
274	C₂×#102	C₂²×C₅	1	1	yes	characteristic
275	C₂×#102	C₂²×C₅	1	1	yes	characteristic
276	C₂×#102	C₂²×C₅	1	1	yes	characteristic
277	C₂×#102	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₂×#102	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
281	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
283	#390	—	2	1	no	—
284	#390	—	2	1	no	—
285	#390	—	2	1	no	—
286	#390	C₂²×C₅	1	1	yes	characteristic
287	#390	C₂²×C₅	1	1	yes	characteristic
288	#390	C₂²×C₅	1	1	yes	characteristic
289	#390	C₂²×C₅	1	1	yes	characteristic
290	#390	C₂²×C₅	1	1	yes	characteristic, complemented
291	#389	C₂²×C₅	1	1	yes	characteristic, complemented
292	#388	—	2	1	no	—
293	#386	—	2	1	no	—
294	#385	—	2	1	no	—
295	#380	C₂²×C₅	1	1	yes	characteristic
296	#379	—	2	1	no	—
297	#379	—	2	1	no	—
298	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
299	#340	C₂²×C₅	1	1	yes	characteristic, complemented
300	#340	C₂²×C₅	1	1	yes	characteristic, complemented
301	#340	C₂²×C₅	1	1	yes	characteristic, complemented
302	#340	C₂²×C₅	1	1	yes	characteristic, complemented
303	#336	C₂²×C₅	1	1	yes	characteristic, complemented
304	#336	C₂²×C₅	1	1	yes	characteristic, complemented
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	2	no	—
312	C₂³×C₅	—	2	2	no	—
313	C₂³×C₅	—	2	2	no	—
314	C₂³×C₅	—	4	8	no	—
315	C₂³×C₅	—	4	1	no	—
316	C₂³×C₅	—	4	1	no	—
317	C₂³×C₅	—	4	1	no	—
318	C₂³×C₅	—	4	1	no	—
319	C₂³×C₅	—	4	1	no	—
320	C₂³×C₅	—	4	1	no	—
321	C₂³×C₅	—	4	1	no	—
322	C₂³×C₅	—	4	1	no	—
323	C₂³×C₅	—	4	1	no	—
324	C₂³×C₅	—	4	1	no	—
325	C₂³×C₅	—	4	1	no	—
326	C₂³×C₅	—	4	1	no	—
327	C₂³×C₅	—	4	1	no	—
328	C₂³×C₅	—	4	1	no	—
329	C₂³×C₅	—	4	1	no	—
330	C₂³×C₅	—	4	1	no	—
331	C₂³×C₅	—	4	1	no	—
332	C₂³×C₅	—	4	1	no	—
333	C₂³×C₅	—	8	4	no	—
334	C₂³×C₅	—	8	4	no	—
335	C₂³×C₅	—	8	4	no	—
336	C₂³×C₅	—	8	4	no	—
337	C₂³×C₅	—	8	4	no	—
338	C₂³×C₅	—	8	4	no	—
339	C₂³×C₅	C₄×D₄	1	2	yes	—
340	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
341	C₅×D₄	—	2	2	no	—
342	C₅×D₄	—	2	2	no	—
343	C₅×D₄	—	2	2	no	—
344	C₅×D₄	—	2	2	no	—
345	C₅×D₄	—	2	2	no	—
346	C₅×D₄	—	2	2	no	—
347	C₅×D₄	—	4	8	no	—
348	C₅×D₄	—	4	1	no	—
349	C₅×D₄	—	4	1	no	—
350	C₅×D₄	—	4	1	no	—
351	C₅×D₄	—	4	1	no	—
352	C₅×D₄	—	4	1	no	—
353	C₅×D₄	—	4	1	no	—
354	C₅×D₄	—	8	4	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	2	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	1	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	4	1	no	—
375	C₂×C₄×C₅	—	4	1	no	—
376	C₂×C₄×C₅	—	4	1	no	—
377	C₂×C₄×C₅	—	4	1	no	—
378	C₂×C₄×C₅	—	4	1	no	—
379	C₂×C₄×C₅	—	4	1	no	—
380	C₂×C₄×C₅	—	4	1	no	—
381	C₂×C₄×C₅	—	4	1	no	—
382	C₂×C₄×C₅	—	4	1	no	—
383	C₂×C₄×C₅	—	4	1	no	—
384	C₂×C₄×C₅	—	4	1	no	—
385	C₂×C₄×C₅	—	4	1	no	—
386	C₂×C₄×C₅	—	4	1	no	—
387	C₂×C₄×C₅	—	4	1	no	—
388	C₂×C₄×C₅	—	8	4	no	—
389	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
390	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
391	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
392	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
393	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
394	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
395	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
396	C₅×C₈	—	2	2	no	—
397	C₅×C₈	—	2	2	no	—
398	C₅×C₈	—	4	1	no	—
399	C₅×C₈	—	4	1	no	—
400	C₂⁵	—	2	1	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	—	2	2	no	—
404	C₂²×D₄	—	4	1	no	—
405	C₂²×D₄	—	4	1	no	—
406	C₂²×D₄	—	4	1	no	—
407	C₂²×D₄	—	4	1	no	—
408	C₂²×D₄	C₂×C₄×C₅	1	4	yes	complemented
409	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
410	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
411	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
412	C₂³×C₄	—	2	1	no	—
413	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂×D₈	—	4	1	no	—
415	C₂×D₈	—	4	1	no	—
416	C₂×D₈	—	4	1	no	—
417	C₂×D₈	—	4	1	no	—
418	C₂×D₈	C₂×C₄×C₅	1	4	yes	—
419	C₂×D₈	C₂×C₄×C₅	1	4	yes	—
420	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
424	#121	—	2	2	no	—
425	#121	C₂×C₄×C₅	1	4	yes	—
426	C₄×D₄	—	4	1	no	—
427	C₄×D₄	—	4	1	no	—
428	#117	—	4	1	no	—
429	#117	—	4	1	no	—
430	#117	—	4	1	no	—
431	#117	—	4	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
460	#107	—	4	1	no	—
461	#106	—	4	1	no	—
462	#102	—	4	1	no	—
463	#102	—	4	1	no	—
464	#102	—	4	1	no	—
465	#102	—	4	1	no	—
466	#102	—	4	1	no	—
467	#102	—	4	1	no	—
468	#102	C₂×C₄×C₅	1	4	yes	complemented
469	#102	C₂×C₄×C₅	1	4	yes	complemented
470	C₂²⋊C₈	—	2	2	no	—
471	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
472	#97	—	4	1	no	—
473	C₄×C₈	—	4	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	C₂²×C₅	—	2	2	no	—
478	C₂²×C₅	—	2	2	no	—
479	C₂²×C₅	—	2	2	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	2	no	—
485	C₂²×C₅	—	4	2	no	—
486	C₂²×C₅	—	4	2	no	—
487	C₂²×C₅	—	4	2	no	—
488	C₂²×C₅	—	4	2	no	—
489	C₂²×C₅	—	4	2	no	—
490	C₂²×C₅	—	4	2	no	—
491	C₂²×C₅	—	4	2	no	—
492	C₂²×C₅	—	4	2	no	—
493	C₂²×C₅	—	8	16	no	—
494	C₂²×C₅	—	8	1	no	—
495	C₂²×C₅	—	8	1	no	—
496	C₂²×C₅	—	8	1	no	—
497	C₂²×C₅	—	8	1	no	—
498	C₂²×C₅	—	8	1	no	—
499	C₂²×C₅	—	8	1	no	—
500	C₂²×C₅	—	8	1	no	—
501	C₂²×C₅	—	8	1	no	—
502	C₂²×C₅	—	8	1	no	—
503	C₂²×C₅	—	8	1	no	—
504	C₂²×C₅	—	8	1	no	—
505	C₂²×C₅	—	8	1	no	—
506	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
507	C₂²×C₅	#534	1	1	yes	characteristic
508	C₂²×C₅	#535	1	1	yes	characteristic
509	C₂²×C₅	#576	1	1	yes	characteristic
510	C₂²×C₅	#576	1	1	yes	characteristic
511	C₂²×C₅	#576	1	1	yes	characteristic
512	C₂²×C₅	#577	1	1	yes	characteristic
513	C₄×C₅	—	2	2	no	—
514	C₄×C₅	—	4	1	no	—
515	C₄×C₅	—	4	1	no	—
516	C₄×C₅	—	4	1	no	—
517	C₄×C₅	—	4	1	no	—
518	C₄×C₅	—	4	2	no	—
519	C₄×C₅	—	8	1	no	—
520	C₄×C₅	—	8	1	no	—
521	C₄×C₅	—	8	1	no	—
522	C₄×C₅	—	8	1	no	—
523	C₄×C₅	#518	1	1	yes	characteristic
524	C₄×C₅	#518	1	1	yes	characteristic
525	C₄×C₅	#538	1	1	yes	characteristic
526	C₄×C₅	#538	1	1	yes	characteristic
527	C₂⁴	—	2	1	no	—
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	1	no	—
530	C₂⁴	—	2	4	no	—
531	C₂⁴	—	4	2	no	—
532	C₂⁴	—	4	2	no	—
533	C₂⁴	—	8	1	no	—
534	C₂⁴	—	8	1	no	—
535	C₂⁴	—	8	1	no	—
536	C₂⁴	—	8	1	no	—
537	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	8	1	no	—
562	C₂×D₄	—	8	1	no	—
563	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
564	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
565	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	8	1	no	—
577	C₂²×C₄	—	8	1	no	—
578	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
579	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
580	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
581	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
582	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
583	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
584	C₂²×C₄	C₅×#41	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
586	D₈	—	4	4	no	—
587	D₈	—	4	4	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
599	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	4	1	no	—
610	C₄⋊C₄	—	4	1	no	—
611	C₄⋊C₄	—	8	1	no	—
612	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	4	1	no	—
615	C₂²⋊C₄	—	4	1	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	8	1	no	—
619	C₂²⋊C₄	—	8	1	no	—
620	C₂²⋊C₄	—	8	1	no	—
621	C₂²⋊C₄	—	8	1	no	—
622	C₂²⋊C₄	—	8	1	no	—
623	C₂²⋊C₄	—	8	1	no	—
624	C₂²⋊C₄	—	8	1	no	—
625	C₂²⋊C₄	—	8	1	no	—
626	C₂²⋊C₄	—	8	1	no	—
627	C₂²⋊C₄	—	8	1	no	—
628	C₂²⋊C₄	—	8	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	—	2	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	2	1	no	—
633	C₄²	—	4	2	no	—
634	C₄²	—	8	1	no	—
635	C₂×C₅	—	4	2	no	—
636	C₂×C₅	—	8	2	no	—
637	C₂×C₅	—	8	2	no	—
638	C₂×C₅	—	8	2	no	—
639	C₂×C₅	#2321	1	1	yes	characteristic
640	C₂×C₅	#2946	1	1	yes	characteristic
641	C₂×C₅	#2948	1	1	yes	characteristic
642	C₂×C₅	#3198	1	1	yes	characteristic
643	C₂×C₅	#3199	1	1	yes	characteristic
644	C₂×C₅	#3220	1	1	yes	characteristic
645	C₂×C₅	#3224	1	1	yes	characteristic
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	4	8	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	8	4	no	—
675	C₂³	—	8	4	no	—
676	C₂³	—	8	4	no	—
677	C₂³	—	8	4	no	—
678	C₂³	—	8	4	no	—
679	C₂³	—	8	4	no	—
680	C₂³	C₄×C₅×D₄	1	2	yes	—
681	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	4	8	no	—
689	D₄	—	4	1	no	—
690	D₄	—	4	1	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	8	4	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	8	4	no	—
730	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
731	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
732	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
733	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
734	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
735	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
736	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
737	C₈	—	2	2	no	—
738	C₈	—	2	2	no	—
739	C₈	—	4	1	no	—
740	C₈	—	4	1	no	—
741	C₅	#22056	1	1	yes	characteristic, direct product factor, Sylow
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	8	16	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	—	8	1	no	—
768	C₂²	—	8	1	no	—
769	C₂²	—	8	1	no	—
770	C₂²	—	8	1	no	—
771	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
772	C₂²	C₅×#534	1	1	yes	characteristic
773	C₂²	C₅×#535	1	1	yes	characteristic
774	C₂²	C₅×#576	1	1	yes	characteristic
775	C₂²	C₅×#576	1	1	yes	characteristic
776	C₂²	C₅×#576	1	1	yes	characteristic
777	C₂²	C₅×#577	1	1	yes	characteristic
778	C₄	—	2	2	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	2	no	—
784	C₄	—	8	1	no	—
785	C₄	—	8	1	no	—
786	C₄	—	8	1	no	—
787	C₄	—	8	1	no	—
788	C₄	C₅×#518	1	1	yes	characteristic
789	C₄	C₅×#518	1	1	yes	characteristic
790	C₄	C₅×#538	1	1	yes	characteristic
791	C₄	C₅×#538	1	1	yes	characteristic
792	C₂	—	4	2	no	—
793	C₂	—	8	2	no	—
794	C₂	—	8	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₅×#2321	1	1	yes	characteristic
797	C₂	C₅×#2946	1	1	yes	characteristic
798	C₂	C₅×#2948	1	1	yes	characteristic
799	C₂	C₅×#3198	1	1	yes	characteristic
800	C₂	C₅×#3199	1	1	yes	characteristic
801	C₂	C₅×#3220	1	1	yes	characteristic
802	C₂	C₅×#3224	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#447	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2324	C₂	semidirect
3. C₅×#2309	C₂	semidirect
4. C₅×#1972	C₂	semidirect
5. C₅×#1970	C₂	semidirect
6. C₅×#1936	C₂	semidirect
7. C₅×#1934	C₂	semidirect
8. C₅×#1926	C₂	semidirect
9. C₅×#1925	C₂	semidirect
10. C₅×#1879	C₂	semidirect
11. C₅×#1879	C₂	semidirect
12. C₅×#1875	C₂	semidirect
13. C₅×#1854	C₂	semidirect
14. C₅×#1786	C₂	semidirect
15. C₅×#1750	C₂	semidirect
20. C₂×C₄×C₅×D₄	C₂²	semidirect
23. C₅×#447	C₄	semidirect
24. C₂×C₅×#107	C₂²	semidirect
25. C₂×C₅×#106	C₂²	semidirect
32. C₂×C₅×#102	C₂²	semidirect
33. C₂×C₅×#102	C₂²	semidirect
36. C₂×C₅×#97	C₂²	semidirect
37. C₂×C₄×C₅×C₈	C₂²	semidirect
45. C₅×#390	C₂²	semidirect
46. C₅×#389	C₂²	semidirect
53. C₄×C₅×C₄⋊C₄	C₂²	semidirect
54. C₅×#340	C₂²	semidirect
55. C₅×#340	C₂²	semidirect
56. C₅×#340	C₂²	semidirect
57. C₅×#340	C₂²	semidirect
58. C₅×#336	C₂²	semidirect
59. C₅×#336	C₂²	semidirect
60. #22056	C₅	direct (N × H)
69. C₂²×C₅×D₄	C₂×C₄	semidirect
129. C₅×#102	C₂×C₄	semidirect
130. C₅×#102	C₂×C₄	semidirect
132. C₅×C₂²⋊C₈	C₂×C₄	semidirect
139. #2324	C₂×C₅	semidirect
140. #2309	C₂×C₅	semidirect
141. #1972	C₂×C₅	semidirect
142. #1970	C₂×C₅	semidirect
143. #1936	C₂×C₅	semidirect
144. #1934	C₂×C₅	semidirect
145. #1926	C₂×C₅	semidirect
146. #1925	C₂×C₅	semidirect
147. #1879	C₂×C₅	semidirect
148. #1879	C₂×C₅	semidirect
149. #1875	C₂×C₅	semidirect
150. #1854	C₂×C₅	semidirect
151. #1786	C₂×C₅	semidirect
152. #1750	C₂×C₅	semidirect
265. C₂×C₄×D₄	C₂²×C₅	semidirect
268. #447	C₄×C₅	semidirect
269. C₂×#107	C₂²×C₅	semidirect
270. C₂×#106	C₂²×C₅	semidirect
277. C₂×#102	C₂²×C₅	semidirect
278. C₂×#102	C₂²×C₅	semidirect
281. C₂×#97	C₂²×C₅	semidirect
282. C₂×C₄×C₈	C₂²×C₅	semidirect
290. #390	C₂²×C₅	semidirect
291. #389	C₂²×C₅	semidirect
298. C₄×C₄⋊C₄	C₂²×C₅	semidirect
299. #340	C₂²×C₅	semidirect
300. #340	C₂²×C₅	semidirect
301. #340	C₂²×C₅	semidirect
302. #340	C₂²×C₅	semidirect
303. #336	C₂²×C₅	semidirect
304. #336	C₂²×C₅	semidirect
408. C₂²×D₄	C₂×C₄×C₅	semidirect
468. #102	C₂×C₄×C₅	semidirect
469. #102	C₂×C₄×C₅	semidirect
471. C₂²⋊C₈	C₂×C₄×C₅	semidirect
741. C₅	#22056	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×#447	2
C₅×#2324	2
C₅×#2309	2
C₅×#1972	2
C₅×#1970	2
C₅×#1936	2
C₅×#1934	2
C₅×#1926	2
C₅×#1925	2
C₅×#1879	2
C₅×#1875	2
C₅×#1854	2
C₅×#1786	2
C₅×#1750	2
#22056	5

Subgroups — C5×#22056 #11944776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22056 #11944776