Subgroups — C₂×C₅×#3125 #11983274

Order 1280.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3125	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#481	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#449	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₅×#542	—	2	4	no	—
23	C₅×#542	C₂²	1	8	yes	complemented
24	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×#126	—	2	1	no	—
26	C₂×C₅×#124	—	2	1	no	—
27	C₂×C₅×#124	C₂²	1	1	yes	characteristic
28	C₂×C₅×#123	—	2	1	no	—
29	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×#121	C₂²	1	1	yes	characteristic
32	C₅×#520	—	2	4	no	—
33	C₅×#520	C₂²	1	8	yes	complemented
34	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×D₄	—	2	1	no	—
38	C₂×C₄×C₅×D₄	—	2	1	no	—
39	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₅×#117	—	2	1	no	—
43	C₂×C₅×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
45	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₅×#483	C₂²	1	8	yes	complemented
47	C₅×#481	C₂²	1	8	yes	complemented
48	C₅×#476	C₂²	1	8	yes	complemented
49	C₅×#475	C₂²	1	8	yes	complemented
50	C₅×#464	C₂²	1	8	yes	complemented
51	C₅×#463	C₂²	1	8	yes	complemented
52	C₅×#452	C₂²	1	8	yes	complemented
53	C₅×#449	C₂²	1	8	yes	—
54	C₅×#442	C₂²	1	8	yes	complemented
55	C₅×#441	C₂²	1	8	yes	complemented
56	C₄×C₅×SD₁₆	C₂²	1	8	yes	complemented
57	C₄×C₅×SD₁₆	C₂²	1	8	yes	complemented
58	C₅×#433	C₂²	1	8	yes	complemented
59	C₂×C₅×#106	C₂²	1	1	yes	characteristic
60	C₂×C₅×#106	C₂²	1	1	yes	characteristic
61	C₂×C₅×#106	C₂²	1	1	yes	characteristic
62	C₂×C₅×#106	C₂²	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₅×#103	C₂²	1	1	yes	characteristic
66	C₂×C₅×#103	C₂²	1	1	yes	characteristic
67	C₂×C₅×#103	C₂²	1	1	yes	characteristic
68	C₂×C₅×#103	C₂²	1	1	yes	characteristic
69	C₂×C₅×#102	C₂²	1	1	yes	characteristic
70	C₂×C₅×#102	C₂²	1	1	yes	characteristic
71	C₂×C₅×#102	C₂²	1	1	yes	characteristic
72	C₂×C₅×#102	C₂²	1	1	yes	characteristic
73	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₅×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
77	C₂×#3125	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂×C₅×#41	—	2	4	no	—
79	C₂×C₅×#41	—	2	4	no	—
80	C₂×C₅×#41	—	2	2	no	—
81	C₂×C₅×#41	C₂³	1	4	yes	—
82	C₂²×C₅×Q₈	—	2	1	no	—
83	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×D₄	—	2	1	no	—
86	C₂²×C₅×D₄	—	2	1	no	—
87	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅	—	2	1	no	—
90	C₂³×C₄×C₅	—	2	1	no	—
91	C₂³×C₄×C₅	—	2	1	no	—
92	C₂³×C₄×C₅	—	2	1	no	—
93	C₂³×C₄×C₅	—	2	1	no	—
94	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₅×Q₁₆	—	2	4	no	—
96	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
97	C₂×C₅×SD₁₆	—	2	4	no	—
98	C₂×C₅×SD₁₆	—	2	4	no	—
99	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₅×D₈	—	2	4	no	—
102	C₂×C₅×D₈	C₂³	1	4	yes	—
103	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₅×C₄⋊Q₈	—	2	2	no	—
108	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
109	C₅×#126	—	2	8	no	—
110	C₅×#124	—	2	8	no	—
111	C₅×#124	—	2	2	no	—
112	C₅×#124	C₂³	1	4	yes	—
113	C₅×#123	—	2	8	no	—
114	C₅×C₂²⋊Q₈	—	2	2	no	—
115	C₅×C₂²⋊Q₈	—	2	8	no	—
116	C₅×C₂²⋊Q₈	C₂³	1	4	yes	—
117	C₅×#121	—	2	2	no	—
118	C₅×#121	C₂³	1	4	yes	—
119	C₄×C₅×Q₈	—	2	2	no	—
120	C₄×C₅×Q₈	—	2	2	no	—
121	C₄×C₅×Q₈	—	2	2	no	—
122	C₄×C₅×Q₈	C₂³	1	4	yes	—
123	C₄×C₅×Q₈	C₂³	1	4	yes	—
124	C₄×C₅×Q₈	C₂³	1	4	yes	—
125	C₄×C₅×D₄	—	2	8	no	—
126	C₄×C₅×D₄	—	2	8	no	—
127	C₄×C₅×D₄	—	2	2	no	—
128	C₄×C₅×D₄	—	2	2	no	—
129	C₄×C₅×D₄	—	2	2	no	—
130	C₄×C₅×D₄	C₂³	1	4	yes	—
131	C₄×C₅×D₄	C₂³	1	4	yes	—
132	C₄×C₅×D₄	C₂³	1	4	yes	—
133	C₅×#117	—	2	8	no	—
134	C₅×#117	D₄	1	4	yes	—
135	C₅×#117	C₂³	1	4	yes	—
136	C₂×C₅×C₄⋊C₄	—	2	1	no	—
137	C₂×C₅×C₄⋊C₄	—	2	1	no	—
138	C₂×C₅×C₄⋊C₄	—	2	1	no	—
139	C₂×C₅×C₄⋊C₄	—	2	2	no	—
140	C₂×C₅×C₄⋊C₄	—	2	1	no	—
141	C₂×C₅×C₄⋊C₄	—	2	1	no	—
142	C₂×C₅×C₄⋊C₄	—	2	1	no	—
143	C₂×C₅×C₄⋊C₄	—	2	8	no	—
144	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
145	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
146	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
151	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
153	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
159	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₅	—	2	1	no	—
161	C₂×C₄²×C₅	—	2	1	no	—
162	C₂×C₄²×C₅	—	2	1	no	—
163	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₅×#106	C₂³	1	4	yes	—
166	C₅×#106	C₂³	1	4	yes	—
167	C₅×#106	C₂³	1	4	yes	—
168	C₅×#106	C₂³	1	4	yes	—
169	C₅×C₄⋊C₈	C₂³	1	4	yes	—
170	C₅×C₄⋊C₈	C₂³	1	4	yes	—
171	C₅×#103	C₂³	1	4	yes	—
172	C₅×#103	C₂³	1	4	yes	—
173	C₅×#103	C₂³	1	4	yes	—
174	C₅×#103	C₂³	1	4	yes	—
175	C₅×#102	C₂³	1	4	yes	—
176	C₅×#102	C₂³	1	4	yes	—
177	C₅×#102	C₂³	1	4	yes	—
178	C₅×#102	C₂³	1	4	yes	—
179	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
181	C₅×#97	C₂³	1	4	yes	—
182	C₄×C₅×C₈	C₂³	1	4	yes	—
183	C₂×#542	C₂×C₅	1	1	yes	characteristic, complemented
184	C₂×#520	C₂×C₅	1	1	yes	characteristic, complemented
185	#3125	C₂×C₅	1	16	yes	direct product factor
186	C₂×#481	C₂×C₅	1	1	yes	characteristic, complemented
187	C₂×#483	C₂×C₅	1	1	yes	characteristic, complemented
188	C₂×#475	C₂×C₅	1	1	yes	characteristic, complemented
189	C₂×#476	C₂×C₅	1	1	yes	characteristic, complemented
190	C₂×#464	C₂×C₅	1	1	yes	characteristic, complemented
191	C₂×#463	C₂×C₅	1	1	yes	characteristic, complemented
192	C₂×#452	C₂×C₅	1	1	yes	characteristic, complemented
193	C₂×#449	C₂×C₅	1	1	yes	characteristic
194	C₂×#442	C₂×C₅	1	1	yes	characteristic, complemented
195	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
196	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
197	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
198	C₂×#433	C₂×C₅	1	1	yes	characteristic, complemented
199	C₂⁴×C₅	—	2	1	no	—
200	C₂⁴×C₅	—	2	1	no	—
201	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
202	C₅×#41	—	2	16	no	—
203	C₅×#41	—	2	8	no	—
204	C₅×#41	—	2	8	no	—
205	C₂×C₅×Q₈	—	2	1	no	—
206	C₂×C₅×Q₈	—	2	1	no	—
207	C₂×C₅×Q₈	—	2	4	no	—
208	C₂×C₅×Q₈	—	2	2	no	—
209	C₂×C₅×Q₈	—	2	2	no	—
210	C₂×C₅×Q₈	—	2	2	no	—
211	C₂×C₅×Q₈	—	8	2	no	—
212	C₂×C₅×Q₈	#41	1	4	yes	—
213	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
214	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
215	C₂×C₅×D₄	—	2	8	no	—
216	C₂×C₅×D₄	—	2	4	no	—
217	C₂×C₅×D₄	—	2	4	no	—
218	C₂×C₅×D₄	—	2	1	no	—
219	C₂×C₅×D₄	—	2	1	no	—
220	C₂×C₅×D₄	—	2	2	no	—
221	C₂×C₅×D₄	—	2	2	no	—
222	C₂×C₅×D₄	—	2	2	no	—
223	C₂×C₅×D₄	—	8	2	no	—
224	C₂×C₅×D₄	#41	1	4	yes	—
225	C₂×C₅×D₄	C₂⁴	1	2	yes	—
226	C₂×C₅×D₄	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₅	—	2	8	no	—
228	C₂²×C₄×C₅	—	2	1	no	—
229	C₂²×C₄×C₅	—	2	4	no	—
230	C₂²×C₄×C₅	—	2	2	no	—
231	C₂²×C₄×C₅	—	2	2	no	—
232	C₂²×C₄×C₅	—	2	1	no	—
233	C₂²×C₄×C₅	—	2	1	no	—
234	C₂²×C₄×C₅	—	2	1	no	—
235	C₂²×C₄×C₅	—	2	1	no	—
236	C₂²×C₄×C₅	—	2	1	no	—
237	C₂²×C₄×C₅	—	2	4	no	—
238	C₂²×C₄×C₅	—	2	4	no	—
239	C₂²×C₄×C₅	—	2	4	no	—
240	C₂²×C₄×C₅	—	2	4	no	—
241	C₂²×C₄×C₅	—	8	2	no	—
242	C₂²×C₄×C₅	—	8	2	no	—
243	C₂²×C₄×C₅	—	8	2	no	—
244	C₂²×C₄×C₅	—	8	2	no	—
245	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
253	C₅×Q₁₆	—	2	8	no	—
254	C₅×SD₁₆	—	2	8	no	—
255	C₅×SD₁₆	—	2	8	no	—
256	C₅×D₈	—	2	8	no	—
257	C₂×C₅×C₈	—	2	2	no	—
258	C₂×C₅×C₈	—	2	2	no	—
259	C₂×C₅×C₈	—	2	2	no	—
260	C₂×C₅×C₈	—	2	2	no	—
261	C₂×C₅×C₈	C₂⁴	1	2	yes	—
262	C₂×C₅×C₈	C₂⁴	1	2	yes	—
263	C₂×C₅×C₈	C₂⁴	1	2	yes	—
264	C₂×C₅×C₈	C₂⁴	1	2	yes	—
265	C₅×C₄⋊C₄	—	2	4	no	—
266	C₅×C₄⋊C₄	—	2	4	no	—
267	C₅×C₄⋊C₄	—	2	4	no	—
268	C₅×C₄⋊C₄	—	2	1	no	—
269	C₅×C₄⋊C₄	—	2	1	no	—
270	C₅×C₄⋊C₄	—	2	4	no	—
271	C₅×C₄⋊C₄	—	2	4	no	—
272	C₅×C₄⋊C₄	—	2	4	no	—
273	C₅×C₄⋊C₄	—	2	1	no	—
274	C₅×C₄⋊C₄	—	2	1	no	—
275	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
276	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
277	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₅×C₂²⋊C₄	—	2	4	no	—
282	C₅×C₂²⋊C₄	—	2	4	no	—
283	C₅×C₂²⋊C₄	—	2	4	no	—
284	C₅×C₂²⋊C₄	—	2	4	no	—
285	C₅×C₂²⋊C₄	—	2	4	no	—
286	C₅×C₂²⋊C₄	—	2	4	no	—
287	C₅×C₂²⋊C₄	—	2	4	no	—
288	C₅×C₂²⋊C₄	C₂×D₄	1	4	yes	—
289	C₅×C₂²⋊C₄	C₂×D₄	1	4	yes	—
290	C₄²×C₅	—	2	4	no	—
291	C₄²×C₅	—	2	4	no	—
292	C₄²×C₅	—	2	4	no	—
293	C₄²×C₅	C₂×D₄	1	2	yes	—
294	C₄²×C₅	C₂×D₄	1	2	yes	—
295	C₄²×C₅	C₂⁴	1	2	yes	—
296	C₄²×C₅	C₂⁴	1	2	yes	—
297	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
298	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
299	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
300	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
301	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
302	#542	—	2	4	no	—
303	#542	C₂²×C₅	1	8	yes	complemented
304	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
305	C₂×#126	—	2	1	no	—
306	C₂×#124	—	2	1	no	—
307	C₂×#124	C₂²×C₅	1	1	yes	characteristic
308	C₂×#123	—	2	1	no	—
309	C₂×C₂²⋊Q₈	—	2	1	no	—
310	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
311	C₂×#121	C₂²×C₅	1	1	yes	characteristic
312	#520	—	2	4	no	—
313	#520	C₂²×C₅	1	8	yes	complemented
314	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
315	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
316	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
317	C₂×C₄×D₄	—	2	1	no	—
318	C₂×C₄×D₄	—	2	1	no	—
319	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
321	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
322	C₂×#117	—	2	1	no	—
323	C₂×#117	C₂²×C₅	1	1	yes	characteristic
324	C₂²×C₄⋊C₄	—	2	1	no	—
325	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
326	#483	C₂²×C₅	1	8	yes	complemented
327	#481	C₂²×C₅	1	8	yes	complemented
328	#476	C₂²×C₅	1	8	yes	complemented
329	#475	C₂²×C₅	1	8	yes	complemented
330	#464	C₂²×C₅	1	8	yes	complemented
331	#463	C₂²×C₅	1	8	yes	complemented
332	#452	C₂²×C₅	1	8	yes	complemented
333	#449	C₂²×C₅	1	8	yes	—
334	#442	C₂²×C₅	1	8	yes	complemented
335	#441	C₂²×C₅	1	8	yes	complemented
336	C₄×SD₁₆	C₂²×C₅	1	8	yes	complemented
337	C₄×SD₁₆	C₂²×C₅	1	8	yes	complemented
338	#433	C₂²×C₅	1	8	yes	complemented
339	C₂×#106	C₂²×C₅	1	1	yes	characteristic
340	C₂×#106	C₂²×C₅	1	1	yes	characteristic
341	C₂×#106	C₂²×C₅	1	1	yes	characteristic
342	C₂×#106	C₂²×C₅	1	1	yes	characteristic
343	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
344	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
345	C₂×#103	C₂²×C₅	1	1	yes	characteristic
346	C₂×#103	C₂²×C₅	1	1	yes	characteristic
347	C₂×#103	C₂²×C₅	1	1	yes	characteristic
348	C₂×#103	C₂²×C₅	1	1	yes	characteristic
349	C₂×#102	C₂²×C₅	1	1	yes	characteristic
350	C₂×#102	C₂²×C₅	1	1	yes	characteristic
351	C₂×#102	C₂²×C₅	1	1	yes	characteristic
352	C₂×#102	C₂²×C₅	1	1	yes	characteristic
353	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
354	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
355	C₂×#97	C₂²×C₅	1	1	yes	characteristic
356	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
357	C₂³×C₅	—	2	2	no	—
358	C₂³×C₅	—	2	4	no	—
359	C₂³×C₅	—	2	2	no	—
360	C₂³×C₅	—	2	2	no	—
361	C₂³×C₅	—	2	2	no	—
362	C₂³×C₅	—	2	2	no	—
363	C₂³×C₅	—	4	2	no	—
364	C₂³×C₅	—	4	2	no	—
365	C₂³×C₅	—	4	2	no	—
366	C₂³×C₅	—	4	2	no	—
367	C₂³×C₅	—	4	2	no	—
368	C₂³×C₅	C₂²×D₄	1	2	yes	—
369	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
370	C₅×Q₈	—	2	4	no	—
371	C₅×Q₈	—	2	2	no	—
372	C₅×Q₈	—	2	2	no	—
373	C₅×Q₈	—	2	2	no	—
374	C₅×Q₈	—	4	2	no	—
375	C₅×Q₈	—	8	4	no	—
376	C₅×Q₈	C₂×#41	1	4	yes	—
377	C₅×D₄	—	2	16	no	—
378	C₅×D₄	—	2	4	no	—
379	C₅×D₄	—	2	2	no	—
380	C₅×D₄	—	2	2	no	—
381	C₅×D₄	—	2	2	no	—
382	C₅×D₄	—	4	2	no	—
383	C₅×D₄	—	8	4	no	—
384	C₅×D₄	C₂×#41	1	4	yes	—
385	C₂×C₄×C₅	—	2	16	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	4	no	—
388	C₂×C₄×C₅	—	2	2	no	—
389	C₂×C₄×C₅	—	2	2	no	—
390	C₂×C₄×C₅	—	2	2	no	—
391	C₂×C₄×C₅	—	2	2	no	—
392	C₂×C₄×C₅	—	2	2	no	—
393	C₂×C₄×C₅	—	2	4	no	—
394	C₂×C₄×C₅	—	2	2	no	—
395	C₂×C₄×C₅	—	2	2	no	—
396	C₂×C₄×C₅	—	2	2	no	—
397	C₂×C₄×C₅	—	2	2	no	—
398	C₂×C₄×C₅	—	2	2	no	—
399	C₂×C₄×C₅	—	2	2	no	—
400	C₂×C₄×C₅	—	2	2	no	—
401	C₂×C₄×C₅	—	4	2	no	—
402	C₂×C₄×C₅	—	4	2	no	—
403	C₂×C₄×C₅	—	4	2	no	—
404	C₂×C₄×C₅	—	4	2	no	—
405	C₂×C₄×C₅	—	4	2	no	—
406	C₂×C₄×C₅	—	8	4	no	—
407	C₂×C₄×C₅	—	8	4	no	—
408	C₂×C₄×C₅	—	8	4	no	—
409	C₂×C₄×C₅	—	8	4	no	—
410	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₅	C₂×#41	1	2	yes	—
417	C₂×C₄×C₅	C₂×#41	1	2	yes	—
418	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
419	C₅×C₈	—	2	2	no	—
420	C₅×C₈	—	2	2	no	—
421	C₅×C₈	—	2	2	no	—
422	C₅×C₈	—	2	2	no	—
423	C₂×#41	—	2	4	no	—
424	C₂×#41	—	2	4	no	—
425	C₂×#41	—	2	2	no	—
426	C₂×#41	C₂³×C₅	1	4	yes	—
427	C₂²×Q₈	—	2	1	no	—
428	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
433	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
440	C₂×Q₁₆	—	2	4	no	—
441	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
442	C₂×SD₁₆	—	2	4	no	—
443	C₂×SD₁₆	—	2	4	no	—
444	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
445	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
446	C₂×D₈	—	2	4	no	—
447	C₂×D₈	C₂³×C₅	1	4	yes	—
448	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
452	C₄⋊Q₈	—	2	2	no	—
453	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
454	#126	—	2	8	no	—
455	#124	—	2	8	no	—
456	#124	—	2	2	no	—
457	#124	C₂³×C₅	1	4	yes	—
458	#123	—	2	8	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	8	no	—
461	C₂²⋊Q₈	C₂³×C₅	1	4	yes	—
462	#121	—	2	2	no	—
463	#121	C₂³×C₅	1	4	yes	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	C₂³×C₅	1	4	yes	—
468	C₄×Q₈	C₂³×C₅	1	4	yes	—
469	C₄×Q₈	C₂³×C₅	1	4	yes	—
470	C₄×D₄	—	2	8	no	—
471	C₄×D₄	—	2	8	no	—
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	—	2	2	no	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	C₂³×C₅	1	4	yes	—
476	C₄×D₄	C₂³×C₅	1	4	yes	—
477	C₄×D₄	C₂³×C₅	1	4	yes	—
478	#117	—	2	8	no	—
479	#117	C₅×D₄	1	4	yes	—
480	#117	C₂³×C₅	1	4	yes	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	2	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	8	no	—
489	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
505	C₂×C₄²	—	2	1	no	—
506	C₂×C₄²	—	2	1	no	—
507	C₂×C₄²	—	2	1	no	—
508	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
510	#106	C₂³×C₅	1	4	yes	—
511	#106	C₂³×C₅	1	4	yes	—
512	#106	C₂³×C₅	1	4	yes	—
513	#106	C₂³×C₅	1	4	yes	—
514	C₄⋊C₈	C₂³×C₅	1	4	yes	—
515	C₄⋊C₈	C₂³×C₅	1	4	yes	—
516	#103	C₂³×C₅	1	4	yes	—
517	#103	C₂³×C₅	1	4	yes	—
518	#103	C₂³×C₅	1	4	yes	—
519	#103	C₂³×C₅	1	4	yes	—
520	#102	C₂³×C₅	1	4	yes	—
521	#102	C₂³×C₅	1	4	yes	—
522	#102	C₂³×C₅	1	4	yes	—
523	#102	C₂³×C₅	1	4	yes	—
524	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
525	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
526	#97	C₂³×C₅	1	4	yes	—
527	C₄×C₈	C₂³×C₅	1	4	yes	—
528	C₂²×C₅	—	2	2	no	—
529	C₂²×C₅	—	2	4	no	—
530	C₂²×C₅	—	2	2	no	—
531	C₂²×C₅	—	2	2	no	—
532	C₂²×C₅	—	4	4	no	—
533	C₂²×C₅	—	4	8	no	—
534	C₂²×C₅	—	4	2	no	—
535	C₂²×C₅	—	4	2	no	—
536	C₂²×C₅	—	4	2	no	—
537	C₂²×C₅	—	4	2	no	—
538	C₂²×C₅	—	4	2	no	—
539	C₂²×C₅	—	8	4	no	—
540	C₂²×C₅	#525	1	2	yes	—
541	C₂²×C₅	#577	1	2	yes	—
542	C₂²×C₅	#577	1	2	yes	—
543	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₅	—	2	2	no	—
545	C₄×C₅	—	2	4	no	—
546	C₄×C₅	—	2	2	no	—
547	C₄×C₅	—	2	2	no	—
548	C₄×C₅	—	2	2	no	—
549	C₄×C₅	—	2	2	no	—
550	C₄×C₅	—	4	2	no	—
551	C₄×C₅	—	4	2	no	—
552	C₄×C₅	—	4	2	no	—
553	C₄×C₅	—	4	2	no	—
554	C₄×C₅	—	4	2	no	—
555	C₄×C₅	#525	1	2	yes	—
556	C₄×C₅	C₂²×#41	1	1	yes	characteristic
557	C₄×C₅	C₂²×#41	1	1	yes	characteristic
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	2	1	no	—
560	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
561	#41	—	2	16	no	—
562	#41	—	2	8	no	—
563	#41	—	2	8	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	8	2	no	—
571	C₂×Q₈	C₅×#41	1	4	yes	—
572	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
573	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
574	C₂×D₄	—	2	8	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	8	2	no	—
583	C₂×D₄	C₅×#41	1	4	yes	—
584	C₂×D₄	C₂⁴×C₅	1	2	yes	—
585	C₂×D₄	C₂⁴×C₅	1	2	yes	—
586	C₂²×C₄	—	2	8	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	8	2	no	—
601	C₂²×C₄	—	8	2	no	—
602	C₂²×C₄	—	8	2	no	—
603	C₂²×C₄	—	8	2	no	—
604	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
605	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
606	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
607	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
608	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
609	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
612	Q₁₆	—	2	8	no	—
613	SD₁₆	—	2	8	no	—
614	SD₁₆	—	2	8	no	—
615	D₈	—	2	8	no	—
616	C₂×C₈	—	2	2	no	—
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	2	2	no	—
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	C₂⁴×C₅	1	2	yes	—
621	C₂×C₈	C₂⁴×C₅	1	2	yes	—
622	C₂×C₈	C₂⁴×C₅	1	2	yes	—
623	C₂×C₈	C₂⁴×C₅	1	2	yes	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
635	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
636	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	C₂×C₅×D₄	1	4	yes	—
648	C₂²⋊C₄	C₂×C₅×D₄	1	4	yes	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	4	no	—
652	C₄²	C₂×C₅×D₄	1	2	yes	—
653	C₄²	C₂×C₅×D₄	1	2	yes	—
654	C₄²	C₂⁴×C₅	1	2	yes	—
655	C₄²	C₂⁴×C₅	1	2	yes	—
656	C₂×C₅	—	4	2	no	—
657	C₂×C₅	—	4	4	no	—
658	C₂×C₅	—	8	2	no	—
659	C₂×C₅	#3125	1	4	yes	direct product factor
660	C₂×C₅	C₂×#525	1	1	yes	characteristic
661	C₂×C₅	C₂×#577	1	1	yes	characteristic
662	C₂×C₅	C₂×#577	1	1	yes	characteristic
663	C₂³	—	2	2	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	C₂²×C₅×D₄	1	2	yes	—
675	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
676	Q₈	—	2	4	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	4	2	no	—
681	Q₈	—	8	4	no	—
682	Q₈	C₂×C₅×#41	1	4	yes	—
683	D₄	—	2	16	no	—
684	D₄	—	2	4	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	4	2	no	—
689	D₄	—	8	4	no	—
690	D₄	C₂×C₅×#41	1	4	yes	—
691	C₂×C₄	—	2	16	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
717	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
718	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
719	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
720	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
721	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
722	C₂×C₄	C₂×C₅×#41	1	2	yes	—
723	C₂×C₄	C₂×C₅×#41	1	2	yes	—
724	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	—	2	2	no	—
728	C₈	—	2	2	no	—
729	C₅	C₂×#3125	1	1	yes	characteristic, direct product factor, Sylow
730	C₂²	—	2	2	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	8	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	8	4	no	—
742	C₂²	C₅×#525	1	2	yes	—
743	C₂²	C₅×#577	1	2	yes	—
744	C₂²	C₅×#577	1	2	yes	—
745	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	C₅×#525	1	2	yes	—
758	C₄	C₂²×C₅×#41	1	1	yes	characteristic
759	C₄	C₂²×C₅×#41	1	1	yes	characteristic
760	C₂	—	4	2	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	C₅×#3125	1	4	yes	direct product factor
764	C₂	C₂×C₅×#525	1	1	yes	characteristic
765	C₂	C₂×C₅×#577	1	1	yes	characteristic
766	C₂	C₂×C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂×C₅×#449	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
1. C₂×C₅×#542	C₂	semidirect
2. C₂×C₅×#520	C₂	semidirect
3. C₅×#3125	C₂	direct (N × H)
4. C₂×C₅×#481	C₂	semidirect
5. C₂×C₅×#483	C₂	semidirect
6. C₂×C₅×#475	C₂	semidirect
7. C₂×C₅×#476	C₂	semidirect
8. C₂×C₅×#464	C₂	semidirect
9. C₂×C₅×#463	C₂	semidirect
10. C₂×C₅×#452	C₂	semidirect
12. C₂×C₅×#442	C₂	semidirect
13. C₂×C₅×#441	C₂	semidirect
14. C₂×C₄×C₅×SD₁₆	C₂	semidirect
15. C₂×C₄×C₅×SD₁₆	C₂	semidirect
16. C₂×C₅×#433	C₂	semidirect
23. C₅×#542	C₂²	semidirect
33. C₅×#520	C₂²	semidirect
46. C₅×#483	C₂²	semidirect
47. C₅×#481	C₂²	semidirect
48. C₅×#476	C₂²	semidirect
49. C₅×#475	C₂²	semidirect
50. C₅×#464	C₂²	semidirect
51. C₅×#463	C₂²	semidirect
52. C₅×#452	C₂²	semidirect
54. C₅×#442	C₂²	semidirect
55. C₅×#441	C₂²	semidirect
56. C₄×C₅×SD₁₆	C₂²	semidirect
57. C₄×C₅×SD₁₆	C₂²	semidirect
58. C₅×#433	C₂²	semidirect
77. C₂×#3125	C₅	direct (N × H)
183. C₂×#542	C₂×C₅	semidirect
184. C₂×#520	C₂×C₅	semidirect
185. #3125	C₂×C₅	direct (N × H)
186. C₂×#481	C₂×C₅	semidirect
187. C₂×#483	C₂×C₅	semidirect
188. C₂×#475	C₂×C₅	semidirect
189. C₂×#476	C₂×C₅	semidirect
190. C₂×#464	C₂×C₅	semidirect
191. C₂×#463	C₂×C₅	semidirect
192. C₂×#452	C₂×C₅	semidirect
194. C₂×#442	C₂×C₅	semidirect
195. C₂×#441	C₂×C₅	semidirect
196. C₂×C₄×SD₁₆	C₂×C₅	semidirect
197. C₂×C₄×SD₁₆	C₂×C₅	semidirect
198. C₂×#433	C₂×C₅	semidirect
303. #542	C₂²×C₅	semidirect
313. #520	C₂²×C₅	semidirect
326. #483	C₂²×C₅	semidirect
327. #481	C₂²×C₅	semidirect
328. #476	C₂²×C₅	semidirect
329. #475	C₂²×C₅	semidirect
330. #464	C₂²×C₅	semidirect
331. #463	C₂²×C₅	semidirect
332. #452	C₂²×C₅	semidirect
334. #442	C₂²×C₅	semidirect
335. #441	C₂²×C₅	semidirect
336. C₄×SD₁₆	C₂²×C₅	semidirect
337. C₄×SD₁₆	C₂²×C₅	semidirect
338. #433	C₂²×C₅	semidirect
659. C₂×C₅	#3125	direct (N × H)
729. C₅	C₂×#3125	direct (N × H)
763. C₂	C₅×#3125	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×#542	2
C₂×C₅×#520	2
C₅×#3125	2
C₂×C₅×#481	2
C₂×C₅×#483	2
C₂×C₅×#475	2
C₂×C₅×#476	2
C₂×C₅×#464	2
C₂×C₅×#463	2
C₂×C₅×#452	2
C₂×C₅×#449	2
C₂×C₅×#442	2
C₂×C₅×#441	2
C₂×C₄×C₅×SD₁₆	2
C₂×C₅×#433	2
C₂×#3125	5

Subgroups — C2×C5×#3125 #11983274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3125 #11983274