Subgroups — C₅×#25950 #11948670

Order 1280.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#102	C₂	1	1	yes	maximal, characteristic
3	C₅×#2440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₅×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2023	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1852	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1808	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1786	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₂²⋊C₄	—	2	1	no	—
24	C₅×#474	—	2	4	no	—
25	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×#102	—	2	4	no	—
32	C₂×C₅×#102	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	C₂²	1	1	yes	characteristic
35	C₂×C₅×#102	C₂²	1	1	yes	characteristic
36	C₂×C₅×#102	C₂²	1	1	yes	characteristic
37	C₂×C₅×#102	C₂²	1	1	yes	characteristic
38	C₂×C₅×#102	C₂²	1	1	yes	characteristic
39	C₂×C₅×#102	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×#398	—	2	1	no	—
42	C₅×#395	—	2	1	no	—
43	C₅×#390	C₂²	1	1	yes	characteristic
44	C₅×#390	C₂²	1	1	yes	characteristic
45	C₅×#389	C₂²	1	1	yes	characteristic, complemented
46	C₅×#389	C₂²	1	1	yes	characteristic, complemented
47	C₅×#386	—	2	1	no	—
48	C₅×#386	—	2	1	no	—
49	C₅×#385	—	2	1	no	—
50	C₅×#384	C₂²	1	1	yes	characteristic, complemented
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₅×#380	C₂²	1	1	yes	characteristic
53	C₅×#379	—	2	1	no	—
54	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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×#340	C₂²	1	1	yes	characteristic, complemented
59	C₅×#336	C₂²	1	1	yes	characteristic, complemented
60	C₅×#336	C₂²	1	1	yes	characteristic, complemented
61	#25950	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁵×C₅	—	2	1	no	—
63	C₂²×C₅×Q₈	—	2	1	no	—
64	C₂²×C₅×D₄	—	2	2	no	—
65	C₂²×C₅×D₄	—	2	2	no	—
66	C₂²×C₅×D₄	—	2	1	no	—
67	C₂²×C₅×D₄	—	2	2	no	—
68	C₂²×C₅×D₄	—	4	1	no	—
69	C₂²×C₅×D₄	—	4	1	no	—
70	C₂²×C₅×D₄	Q₈	1	4	yes	complemented
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	—	2	1	no	—
75	C₂³×C₄×C₅	—	2	1	no	—
76	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	—	2	2	no	—
78	C₂²×C₅×C₈	—	2	2	no	—
79	C₂²×C₅×C₈	—	4	1	no	—
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×C₄⋊Q₈	—	2	2	no	—
85	C₅×C₄⋊Q₈	—	4	1	no	—
86	C₅×C₂²⋊Q₈	—	4	4	no	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₄×C₅×D₄	—	4	1	no	—
90	C₄×C₅×D₄	—	4	1	no	—
91	C₂×C₅×C₄⋊C₄	—	2	2	no	—
92	C₂×C₅×C₄⋊C₄	—	2	1	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	—	2	1	no	—
95	C₂×C₅×C₄⋊C₄	—	2	1	no	—
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	—	4	1	no	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	4	4	no	—
114	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
115	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₅×#107	—	2	2	no	—
119	C₅×#107	—	2	2	no	—
120	C₅×#107	—	4	1	no	—
121	C₅×#107	—	4	1	no	—
122	C₅×C₄⋊C₈	—	2	2	no	—
123	C₅×C₄⋊C₈	—	4	1	no	—
124	C₅×#102	—	2	2	no	—
125	C₅×#102	—	2	2	no	—
126	C₅×#102	—	2	2	no	—
127	C₅×#102	—	2	2	no	—
128	C₅×#102	—	2	2	no	—
129	C₅×#102	—	4	1	no	—
130	C₅×#102	—	4	1	no	—
131	C₅×#102	D₄	1	4	yes	—
132	C₅×C₂²⋊C₈	—	2	2	no	—
133	C₅×#95	—	2	1	no	—
134	C₅×#95	—	2	1	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	—	2	1	no	—
137	C₅×#95	D₄	1	1	yes	characteristic
138	C₅×#95	D₄	1	1	yes	characteristic
139	C₂×#474	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂²×#102	C₂×C₅	1	1	yes	characteristic
141	#2440	C₂×C₅	1	1	yes	characteristic, complemented
142	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
143	#2093	C₂×C₅	1	1	yes	characteristic, complemented
144	#2067	C₂×C₅	1	1	yes	characteristic, complemented
145	#2067	C₂×C₅	1	1	yes	characteristic, complemented
146	#2023	C₂×C₅	1	1	yes	characteristic, complemented
147	#1862	C₂×C₅	1	1	yes	characteristic, complemented
148	#1862	C₂×C₅	1	1	yes	characteristic, complemented
149	#1852	C₂×C₅	1	1	yes	characteristic, complemented
150	#1850	C₂×C₅	1	1	yes	characteristic, complemented
151	#1808	C₂×C₅	1	1	yes	characteristic, complemented
152	#1802	C₂×C₅	1	1	yes	characteristic, complemented
153	#1786	C₂×C₅	1	1	yes	characteristic
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	—	4	2	no	—
160	C₂⁴×C₅	—	4	2	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×Q₈	—	4	2	no	—
165	C₂×C₅×Q₈	—	4	2	no	—
166	C₂×C₅×Q₈	—	8	1	no	—
167	C₂×C₅×D₄	—	2	8	no	—
168	C₂×C₅×D₄	—	2	4	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	—	4	4	no	—
178	C₂×C₅×D₄	—	4	4	no	—
179	C₂×C₅×D₄	—	4	4	no	—
180	C₂×C₅×D₄	—	4	2	no	—
181	C₂×C₅×D₄	—	4	2	no	—
182	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
183	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
184	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
185	C₂×C₅×D₄	#41	1	2	yes	—
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	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
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	—	4	2	no	—
197	C₂²×C₄×C₅	—	4	2	no	—
198	C₂²×C₄×C₅	—	4	2	no	—
199	C₂²×C₄×C₅	—	4	2	no	—
200	C₂²×C₄×C₅	—	4	2	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	—	8	1	no	—
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	C₂×Q₈	1	2	yes	—
211	C₂²×C₄×C₅	#41	1	2	yes	—
212	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	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	—	2	1	no	—
236	C₅×C₄⋊C₄	—	2	1	no	—
237	C₅×C₄⋊C₄	—	4	2	no	—
238	C₅×C₄⋊C₄	—	4	2	no	—
239	C₅×C₄⋊C₄	—	4	2	no	—
240	C₅×C₄⋊C₄	—	4	2	no	—
241	C₅×C₄⋊C₄	—	4	2	no	—
242	C₅×C₄⋊C₄	—	8	1	no	—
243	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
244	C₅×C₂²⋊C₄	—	2	2	no	—
245	C₅×C₂²⋊C₄	—	4	2	no	—
246	C₅×C₂²⋊C₄	—	4	2	no	—
247	C₅×C₂²⋊C₄	—	4	2	no	—
248	C₅×C₂²⋊C₄	—	4	2	no	—
249	C₅×C₂²⋊C₄	—	4	2	no	—
250	C₅×C₂²⋊C₄	—	4	2	no	—
251	C₅×C₂²⋊C₄	—	8	1	no	—
252	C₅×C₂²⋊C₄	—	8	1	no	—
253	C₅×C₂²⋊C₄	D₈	1	4	yes	—
254	C₄²×C₅	—	2	1	no	—
255	C₄²×C₅	—	2	1	no	—
256	C₄²×C₅	—	2	1	no	—
257	C₄²×C₅	—	2	1	no	—
258	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
259	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₂×C₂²⋊Q₈	—	2	1	no	—
262	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	—	2	1	no	—
266	#474	—	2	4	no	—
267	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₂×#102	—	2	4	no	—
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
278	C₂×#102	C₂²×C₅	1	1	yes	characteristic
279	C₂×#102	C₂²×C₅	1	1	yes	characteristic
280	C₂×#102	C₂²×C₅	1	1	yes	characteristic
281	C₂×#102	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	#398	—	2	1	no	—
284	#395	—	2	1	no	—
285	#390	C₂²×C₅	1	1	yes	characteristic
286	#390	C₂²×C₅	1	1	yes	characteristic
287	#389	C₂²×C₅	1	1	yes	characteristic, complemented
288	#389	C₂²×C₅	1	1	yes	characteristic, complemented
289	#386	—	2	1	no	—
290	#386	—	2	1	no	—
291	#385	—	2	1	no	—
292	#384	C₂²×C₅	1	1	yes	characteristic, complemented
293	#380	C₂²×C₅	1	1	yes	characteristic
294	#380	C₂²×C₅	1	1	yes	characteristic
295	#379	—	2	1	no	—
296	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
297	#340	C₂²×C₅	1	1	yes	characteristic, complemented
298	#340	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	#336	C₂²×C₅	1	1	yes	characteristic, complemented
302	#336	C₂²×C₅	1	1	yes	characteristic, complemented
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	2	no	—
308	C₂³×C₅	—	2	2	no	—
309	C₂³×C₅	—	2	2	no	—
310	C₂³×C₅	—	2	2	no	—
311	C₂³×C₅	—	4	8	no	—
312	C₂³×C₅	—	4	1	no	—
313	C₂³×C₅	—	4	1	no	—
314	C₂³×C₅	—	4	1	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	8	no	—
323	C₂³×C₅	—	8	4	no	—
324	C₂³×C₅	—	8	4	no	—
325	C₂³×C₅	—	8	4	no	—
326	C₂³×C₅	—	8	4	no	—
327	C₂³×C₅	—	8	4	no	—
328	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
329	C₂³×C₅	C₂×D₈	1	2	yes	—
330	C₂³×C₅	#137	1	2	yes	—
331	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
332	C₅×Q₈	—	8	4	no	—
333	C₅×D₄	—	2	2	no	—
334	C₅×D₄	—	2	2	no	—
335	C₅×D₄	—	2	2	no	—
336	C₅×D₄	—	2	2	no	—
337	C₅×D₄	—	2	2	no	—
338	C₅×D₄	—	4	8	no	—
339	C₅×D₄	—	4	1	no	—
340	C₅×D₄	—	4	1	no	—
341	C₅×D₄	C₂²⋊Q₈	1	4	yes	complemented
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	2	no	—
349	C₂×C₄×C₅	—	2	2	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	2	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	—	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	—	4	1	no	—
367	C₂×C₄×C₅	—	4	1	no	—
368	C₂×C₄×C₅	—	4	1	no	—
369	C₂×C₄×C₅	—	4	1	no	—
370	C₂×C₄×C₅	—	4	1	no	—
371	C₂×C₄×C₅	—	4	1	no	—
372	C₂×C₄×C₅	—	4	1	no	—
373	C₂×C₄×C₅	—	4	1	no	—
374	C₂×C₄×C₅	—	4	1	no	—
375	C₂×C₄×C₅	—	4	1	no	—
376	C₂×C₄×C₅	—	8	4	no	—
377	C₂×C₄×C₅	—	8	4	no	—
378	C₂×C₄×C₅	—	8	4	no	—
379	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
380	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
381	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
382	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
384	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
385	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
386	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
387	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
388	C₅×C₈	—	2	2	no	—
389	C₅×C₈	—	4	1	no	—
390	C₅×C₈	—	4	1	no	—
391	C₅×C₈	—	4	1	no	—
392	C₂⁵	—	2	1	no	—
393	C₂²×Q₈	—	2	1	no	—
394	C₂²×D₄	—	2	2	no	—
395	C₂²×D₄	—	2	2	no	—
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	—	2	2	no	—
398	C₂²×D₄	—	4	1	no	—
399	C₂²×D₄	—	4	1	no	—
400	C₂²×D₄	C₅×Q₈	1	4	yes	complemented
401	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
402	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
403	C₂³×C₄	—	2	1	no	—
404	C₂³×C₄	—	2	1	no	—
405	C₂³×C₄	—	2	1	no	—
406	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
407	C₂²×C₈	—	2	2	no	—
408	C₂²×C₈	—	2	2	no	—
409	C₂²×C₈	—	4	1	no	—
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⋊Q₈	—	2	2	no	—
415	C₄⋊Q₈	—	4	1	no	—
416	C₂²⋊Q₈	—	4	4	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	4	1	no	—
420	C₄×D₄	—	4	1	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	4	1	no	—
429	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	4	4	no	—
444	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
448	#107	—	2	2	no	—
449	#107	—	2	2	no	—
450	#107	—	4	1	no	—
451	#107	—	4	1	no	—
452	C₄⋊C₈	—	2	2	no	—
453	C₄⋊C₈	—	4	1	no	—
454	#102	—	2	2	no	—
455	#102	—	2	2	no	—
456	#102	—	2	2	no	—
457	#102	—	2	2	no	—
458	#102	—	2	2	no	—
459	#102	—	4	1	no	—
460	#102	—	4	1	no	—
461	#102	C₅×D₄	1	4	yes	—
462	C₂²⋊C₈	—	2	2	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	C₅×D₄	1	1	yes	characteristic
468	#95	C₅×D₄	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	—	2	4	no	—
476	C₂²×C₅	—	4	2	no	—
477	C₂²×C₅	—	4	2	no	—
478	C₂²×C₅	—	4	2	no	—
479	C₂²×C₅	—	4	2	no	—
480	C₂²×C₅	—	4	2	no	—
481	C₂²×C₅	—	4	2	no	—
482	C₂²×C₅	—	4	2	no	—
483	C₂²×C₅	—	4	2	no	—
484	C₂²×C₅	—	4	2	no	—
485	C₂²×C₅	—	8	16	no	—
486	C₂²×C₅	—	8	1	no	—
487	C₂²×C₅	—	8	1	no	—
488	C₂²×C₅	—	8	1	no	—
489	C₂²×C₅	—	8	1	no	—
490	C₂²×C₅	#474	1	4	yes	complemented
491	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
492	C₂²×C₅	D₄²	1	1	yes	characteristic
493	C₂²×C₅	#546	1	1	yes	characteristic
494	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
495	C₂²×C₅	C₂×#137	1	1	yes	characteristic
496	C₂²×C₅	#576	1	1	yes	characteristic
497	C₂²×C₅	#577	1	1	yes	characteristic
498	C₄×C₅	—	2	2	no	—
499	C₄×C₅	—	2	2	no	—
500	C₄×C₅	—	2	2	no	—
501	C₄×C₅	—	4	1	no	—
502	C₄×C₅	—	4	2	no	—
503	C₄×C₅	—	4	1	no	—
504	C₄×C₅	—	8	1	no	—
505	C₄×C₅	—	8	1	no	—
506	C₄×C₅	—	8	1	no	—
507	C₄×C₅	—	8	1	no	—
508	C₄×C₅	—	8	1	no	—
509	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
510	C₄×C₅	#543	1	1	yes	characteristic
511	C₄×C₅	#546	1	1	yes	characteristic
512	C₄×C₅	#551	1	1	yes	characteristic
513	C₂⁴	—	2	1	no	—
514	C₂⁴	—	2	1	no	—
515	C₂⁴	—	2	4	no	—
516	C₂⁴	—	4	2	no	—
517	C₂⁴	—	4	2	no	—
518	C₂⁴	—	4	2	no	—
519	C₂⁴	—	4	2	no	—
520	C₂⁴	—	8	1	no	—
521	C₂⁴	—	8	1	no	—
522	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
523	C₂×Q₈	—	4	2	no	—
524	C₂×Q₈	—	4	2	no	—
525	C₂×Q₈	—	8	1	no	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	4	4	no	—
537	C₂×D₄	—	4	4	no	—
538	C₂×D₄	—	4	4	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
542	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
543	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
544	C₂×D₄	C₅×#41	1	2	yes	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	8	1	no	—
562	C₂²×C₄	—	8	1	no	—
563	C₂²×C₄	—	8	1	no	—
564	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
565	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
566	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
567	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
568	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
569	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
570	C₂²×C₄	C₅×#41	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
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	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	4	4	no	—
584	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	4	2	no	—
597	C₄⋊C₄	—	4	2	no	—
598	C₄⋊C₄	—	4	2	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	—	4	2	no	—
601	C₄⋊C₄	—	8	1	no	—
602	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	4	2	no	—
607	C₂²⋊C₄	—	4	2	no	—
608	C₂²⋊C₄	—	4	2	no	—
609	C₂²⋊C₄	—	4	2	no	—
610	C₂²⋊C₄	—	8	1	no	—
611	C₂²⋊C₄	—	8	1	no	—
612	C₂²⋊C₄	C₅×D₈	1	4	yes	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₂×C₅	—	2	4	no	—
618	C₂×C₅	—	4	4	no	—
619	C₂×C₅	—	8	2	no	—
620	C₂×C₅	#2437	1	1	yes	characteristic
621	C₂×C₅	C₂×#474	1	1	yes	characteristic
622	C₂×C₅	#3081	1	1	yes	characteristic
623	C₂×C₅	#3266	1	1	yes	characteristic
624	C₂×C₅	D₄×D₈	1	1	yes	characteristic
625	C₂×C₅	#3294	1	1	yes	characteristic
626	C₂×C₅	#3314	1	1	yes	characteristic
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	4	8	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	8	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	8	4	no	—
648	C₂³	—	8	4	no	—
649	C₂³	—	8	4	no	—
650	C₂³	—	8	4	no	—
651	C₂³	—	8	4	no	—
652	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
653	C₂³	C₂×C₅×D₈	1	2	yes	—
654	C₂³	C₅×#137	1	2	yes	—
655	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
656	Q₈	—	8	4	no	—
657	D₄	—	2	2	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	2	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	8	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	C₅×C₂²⋊Q₈	1	4	yes	complemented
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	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
704	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
705	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
706	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
707	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
708	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
709	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
710	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
711	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
712	C₈	—	2	2	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₅	#25950	1	1	yes	characteristic, direct product factor, Sylow
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	8	16	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	—	8	1	no	—
737	C₂²	—	8	1	no	—
738	C₂²	C₅×#474	1	4	yes	complemented
739	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
740	C₂²	C₅×D₄²	1	1	yes	characteristic
741	C₂²	C₅×#546	1	1	yes	characteristic
742	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
743	C₂²	C₂×C₅×#137	1	1	yes	characteristic
744	C₂²	C₅×#576	1	1	yes	characteristic
745	C₂²	C₅×#577	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	1	no	—
752	C₄	—	8	1	no	—
753	C₄	—	8	1	no	—
754	C₄	—	8	1	no	—
755	C₄	—	8	1	no	—
756	C₄	—	8	1	no	—
757	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
758	C₄	C₅×#543	1	1	yes	characteristic
759	C₄	C₅×#546	1	1	yes	characteristic
760	C₄	C₅×#551	1	1	yes	characteristic
761	C₂	—	2	4	no	—
762	C₂	—	4	4	no	—
763	C₂	—	8	2	no	—
764	C₂	C₅×#2437	1	1	yes	characteristic
765	C₂	C₂×C₅×#474	1	1	yes	characteristic
766	C₂	C₅×#3081	1	1	yes	characteristic
767	C₂	C₅×#3266	1	1	yes	characteristic
768	C₂	C₅×D₄×D₈	1	1	yes	characteristic
769	C₂	C₅×#3294	1	1	yes	characteristic
770	C₂	C₅×#3314	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#474	C₂	semidirect
3. C₅×#2440	C₂	semidirect
5. C₅×#2093	C₂	semidirect
6. C₅×#2067	C₂	semidirect
7. C₅×#2067	C₂	semidirect
8. C₅×#2023	C₂	semidirect
9. C₅×#1862	C₂	semidirect
10. C₅×#1862	C₂	semidirect
11. C₅×#1852	C₂	semidirect
12. C₅×#1850	C₂	semidirect
13. C₅×#1808	C₂	semidirect
14. C₅×#1802	C₂	semidirect
18. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₅×#107	C₂²	semidirect
26. C₂×C₅×#107	C₂²	semidirect
27. C₂×C₅×#107	C₂²	semidirect
28. C₂×C₅×#107	C₂²	semidirect
29. C₂×C₅×C₄⋊C₈	C₂²	semidirect
30. C₂×C₅×C₄⋊C₈	C₂²	semidirect
45. C₅×#389	C₂²	semidirect
46. C₅×#389	C₂²	semidirect
50. C₅×#384	C₂²	semidirect
55. C₅×#340	C₂²	semidirect
56. C₅×#340	C₂²	semidirect
57. C₅×#340	C₂²	semidirect
58. C₅×#340	C₂²	semidirect
59. C₅×#336	C₂²	semidirect
60. C₅×#336	C₂²	semidirect
61. #25950	C₅	direct (N × H)
70. C₂²×C₅×D₄	Q₈	semidirect
139. C₂×#474	C₂×C₅	semidirect
141. #2440	C₂×C₅	semidirect
143. #2093	C₂×C₅	semidirect
144. #2067	C₂×C₅	semidirect
145. #2067	C₂×C₅	semidirect
146. #2023	C₂×C₅	semidirect
147. #1862	C₂×C₅	semidirect
148. #1862	C₂×C₅	semidirect
149. #1852	C₂×C₅	semidirect
150. #1850	C₂×C₅	semidirect
151. #1808	C₂×C₅	semidirect
152. #1802	C₂×C₅	semidirect
260. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
267. C₂×#107	C₂²×C₅	semidirect
268. C₂×#107	C₂²×C₅	semidirect
269. C₂×#107	C₂²×C₅	semidirect
270. C₂×#107	C₂²×C₅	semidirect
271. C₂×C₄⋊C₈	C₂²×C₅	semidirect
272. C₂×C₄⋊C₈	C₂²×C₅	semidirect
287. #389	C₂²×C₅	semidirect
288. #389	C₂²×C₅	semidirect
292. #384	C₂²×C₅	semidirect
297. #340	C₂²×C₅	semidirect
298. #340	C₂²×C₅	semidirect
299. #340	C₂²×C₅	semidirect
300. #340	C₂²×C₅	semidirect
301. #336	C₂²×C₅	semidirect
302. #336	C₂²×C₅	semidirect
341. C₅×D₄	C₂²⋊Q₈	semidirect
400. C₂²×D₄	C₅×Q₈	semidirect
490. C₂²×C₅	#474	semidirect
665. D₄	C₅×C₂²⋊Q₈	semidirect
716. C₅	#25950	direct (N × H)
738. C₂²	C₅×#474	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#474	2
C₂²×C₅×#102	2
C₅×#2440	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2093	2
C₅×#2067	2
C₅×#2023	2
C₅×#1862	2
C₅×#1852	2
C₅×#1850	2
C₅×#1808	2
C₅×#1802	2
C₅×#1786	2
#25950	5

Subgroups — C5×#25950 #11948670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25950 #11948670