Subgroups — C₅×#25173 #11947893

Order 1280.

1046 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#451	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#451	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2429	C₂	1	1	yes	maximal, characteristic
6	C₅×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
7	C₅×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2035	C₂	1	1	yes	maximal, characteristic
9	C₅×#2035	C₂	1	1	yes	maximal, characteristic
10	C₅×#2016	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1971	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1924	C₂	1	1	yes	maximal, characteristic
13	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₅×#462	—	2	4	no	—
28	C₅×#451	—	2	4	no	—
29	C₅×#451	—	2	4	no	—
30	C₅×#441	—	2	4	no	—
31	C₂×C₅×#106	C₂²	1	1	yes	characteristic
32	C₂×C₅×#106	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×#103	C₂²	1	1	yes	characteristic
35	C₂×C₅×#103	C₂²	1	1	yes	characteristic
36	C₂×C₅×#103	C₂²	1	1	yes	characteristic
37	C₂×C₅×#103	C₂²	1	1	yes	characteristic
38	C₂×C₅×#103	C₂²	1	1	yes	characteristic
39	C₂×C₅×#103	C₂²	1	1	yes	characteristic
40	C₂×C₅×#103	C₂²	1	1	yes	characteristic
41	C₂×C₅×#103	C₂²	1	1	yes	characteristic
42	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₅×#97	C₂²	1	1	yes	characteristic
45	C₅×#398	—	2	1	no	—
46	C₅×#396	—	2	1	no	—
47	C₅×#391	—	2	1	no	—
48	C₅×#391	—	2	1	no	—
49	C₅×#391	C₂²	1	1	yes	characteristic
50	C₅×#391	C₂²	1	1	yes	characteristic
51	C₅×#391	C₂²	1	1	yes	characteristic
52	C₅×#389	—	2	1	no	—
53	C₅×#389	C₂²	1	1	yes	characteristic
54	C₅×#388	—	2	1	no	—
55	C₅×#380	—	2	1	no	—
56	C₅×#380	C₂²	1	1	yes	characteristic
57	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
58	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₅×#340	C₂²	1	1	yes	characteristic
60	C₅×#340	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	C₅×#336	C₂²	1	1	yes	characteristic
63	#25173	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₅×Q₈	—	2	2	no	—
65	C₂²×C₅×Q₈	—	2	2	no	—
66	C₂²×C₅×Q₈	—	2	1	no	—
67	C₂²×C₅×Q₈	—	2	2	no	—
68	C₂²×C₅×Q₈	—	2	2	no	—
69	C₂²×C₅×Q₈	—	4	1	no	—
70	C₂²×C₅×Q₈	—	4	1	no	—
71	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅	—	2	1	no	—
76	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₅×Q₁₆	—	2	2	no	—
78	C₂×C₅×Q₁₆	—	2	2	no	—
79	C₂×C₅×Q₁₆	—	2	2	no	—
80	C₂×C₅×Q₁₆	—	2	2	no	—
81	C₂×C₅×Q₁₆	—	2	2	no	—
82	C₂×C₅×Q₁₆	—	2	2	no	—
83	C₂×C₅×Q₁₆	—	2	2	no	—
84	C₂×C₅×Q₁₆	—	2	2	no	—
85	C₂×C₅×Q₁₆	—	2	2	no	—
86	C₂×C₅×Q₁₆	—	4	1	no	—
87	C₂×C₅×Q₁₆	—	4	1	no	—
88	C₂×C₅×Q₁₆	D₄	1	4	yes	—
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₅×C₄⋊Q₈	—	2	2	no	—
94	C₅×C₄⋊Q₈	—	4	1	no	—
95	C₅×C₂²⋊Q₈	—	2	2	no	—
96	C₅×C₂²⋊Q₈	—	2	2	no	—
97	C₅×C₂²⋊Q₈	—	4	1	no	—
98	C₅×C₂²⋊Q₈	—	4	1	no	—
99	C₄×C₅×Q₈	—	2	2	no	—
100	C₄×C₅×Q₈	—	2	2	no	—
101	C₄×C₅×Q₈	—	2	2	no	—
102	C₄×C₅×Q₈	—	4	1	no	—
103	C₄×C₅×Q₈	—	4	1	no	—
104	C₄×C₅×Q₈	—	4	1	no	—
105	C₂×C₅×C₄⋊C₄	—	2	1	no	—
106	C₂×C₅×C₄⋊C₄	—	2	1	no	—
107	C₂×C₅×C₄⋊C₄	—	2	1	no	—
108	C₂×C₅×C₄⋊C₄	—	2	1	no	—
109	C₂×C₅×C₄⋊C₄	—	2	1	no	—
110	C₂×C₅×C₄⋊C₄	—	2	1	no	—
111	C₂×C₅×C₄⋊C₄	—	2	1	no	—
112	C₂×C₅×C₄⋊C₄	—	2	1	no	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
121	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₅	—	2	1	no	—
123	C₂×C₄²×C₅	—	2	1	no	—
124	C₂×C₄²×C₅	—	2	1	no	—
125	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
127	C₅×#106	—	2	2	no	—
128	C₅×#106	—	4	1	no	—
129	C₅×C₄⋊C₈	—	2	2	no	—
130	C₅×#103	—	2	2	no	—
131	C₅×#103	—	2	2	no	—
132	C₅×#103	—	2	2	no	—
133	C₅×#103	—	2	2	no	—
134	C₅×#103	—	2	2	no	—
135	C₅×#103	—	2	2	no	—
136	C₅×#103	—	4	1	no	—
137	C₅×#103	D₄	1	4	yes	—
138	C₅×C₂²⋊C₈	—	2	2	no	—
139	C₅×C₂²⋊C₈	—	2	2	no	—
140	C₅×#97	—	2	2	no	—
141	C₅×#95	—	2	1	no	—
142	C₅×#95	—	2	1	no	—
143	C₅×#95	—	2	1	no	—
144	C₅×#95	—	2	1	no	—
145	C₅×#95	—	2	1	no	—
146	C₅×#95	—	2	1	no	—
147	C₅×#95	—	2	1	no	—
148	C₅×#95	—	2	1	no	—
149	C₅×#95	D₄	1	1	yes	characteristic
150	C₅×#95	D₄	1	1	yes	characteristic
151	C₂×#462	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×#451	C₂×C₅	1	1	yes	characteristic
153	C₂×#451	C₂×C₅	1	1	yes	characteristic
154	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
155	#2429	C₂×C₅	1	1	yes	characteristic
156	Q₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
157	#2066	C₂×C₅	1	1	yes	characteristic, complemented
158	#2035	C₂×C₅	1	1	yes	characteristic
159	#2035	C₂×C₅	1	1	yes	characteristic
160	#2016	C₂×C₅	1	1	yes	characteristic, complemented
161	#1971	C₂×C₅	1	1	yes	characteristic, complemented
162	#1924	C₂×C₅	1	1	yes	characteristic
163	#1878	C₂×C₅	1	1	yes	characteristic, complemented
164	#1878	C₂×C₅	1	1	yes	characteristic, complemented
165	#1865	C₂×C₅	1	1	yes	characteristic, complemented
166	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂×C₅×Q₈	—	2	4	no	—
168	C₂×C₅×Q₈	—	2	1	no	—
169	C₂×C₅×Q₈	—	2	1	no	—
170	C₂×C₅×Q₈	—	2	1	no	—
171	C₂×C₅×Q₈	—	2	1	no	—
172	C₂×C₅×Q₈	—	2	1	no	—
173	C₂×C₅×Q₈	—	2	1	no	—
174	C₂×C₅×Q₈	—	2	1	no	—
175	C₂×C₅×Q₈	—	2	1	no	—
176	C₂×C₅×Q₈	—	2	1	no	—
177	C₂×C₅×Q₈	—	2	1	no	—
178	C₂×C₅×Q₈	—	2	1	no	—
179	C₂×C₅×Q₈	—	2	1	no	—
180	C₂×C₅×Q₈	—	2	1	no	—
181	C₂×C₅×Q₈	—	2	1	no	—
182	C₂×C₅×Q₈	—	2	1	no	—
183	C₂×C₅×Q₈	—	2	1	no	—
184	C₂×C₅×Q₈	—	2	1	no	—
185	C₂×C₅×Q₈	—	2	1	no	—
186	C₂×C₅×Q₈	—	2	1	no	—
187	C₂×C₅×Q₈	—	4	2	no	—
188	C₂×C₅×Q₈	—	4	2	no	—
189	C₂×C₅×Q₈	—	4	4	no	—
190	C₂×C₅×Q₈	—	4	4	no	—
191	C₂×C₅×Q₈	—	4	4	no	—
192	C₂×C₅×Q₈	—	4	4	no	—
193	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
194	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
195	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
196	C₂×C₅×Q₈	#41	1	2	yes	—
197	C₂×C₅×Q₈	#41	1	2	yes	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	2	4	no	—
200	C₂²×C₄×C₅	—	2	1	no	—
201	C₂²×C₄×C₅	—	2	1	no	—
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	2	1	no	—
206	C₂²×C₄×C₅	—	2	1	no	—
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	—	2	1	no	—
209	C₂²×C₄×C₅	—	2	1	no	—
210	C₂²×C₄×C₅	—	2	1	no	—
211	C₂²×C₄×C₅	—	2	1	no	—
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	4	2	no	—
214	C₂²×C₄×C₅	—	4	2	no	—
215	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
221	C₅×Q₁₆	—	2	8	no	—
222	C₅×Q₁₆	—	4	4	no	—
223	C₅×Q₁₆	—	4	4	no	—
224	C₅×Q₁₆	—	4	4	no	—
225	C₂×C₅×C₈	—	2	1	no	—
226	C₂×C₅×C₈	—	2	1	no	—
227	C₂×C₅×C₈	—	2	1	no	—
228	C₂×C₅×C₈	—	2	1	no	—
229	C₂×C₅×C₈	—	2	1	no	—
230	C₂×C₅×C₈	—	2	1	no	—
231	C₂×C₅×C₈	—	2	1	no	—
232	C₂×C₅×C₈	—	2	1	no	—
233	C₂×C₅×C₈	—	2	1	no	—
234	C₂×C₅×C₈	—	2	1	no	—
235	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
236	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
237	C₅×C₄⋊C₄	—	2	1	no	—
238	C₅×C₄⋊C₄	—	2	1	no	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	2	1	no	—
241	C₅×C₄⋊C₄	—	2	1	no	—
242	C₅×C₄⋊C₄	—	2	1	no	—
243	C₅×C₄⋊C₄	—	2	1	no	—
244	C₅×C₄⋊C₄	—	4	2	no	—
245	C₅×C₄⋊C₄	—	4	2	no	—
246	C₅×C₄⋊C₄	—	4	2	no	—
247	C₅×C₄⋊C₄	—	4	2	no	—
248	C₅×C₄⋊C₄	—	4	2	no	—
249	C₅×C₄⋊C₄	—	4	2	no	—
250	C₅×C₄⋊C₄	—	4	2	no	—
251	C₅×C₄⋊C₄	—	4	2	no	—
252	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
253	C₅×C₂²⋊C₄	—	2	2	no	—
254	C₅×C₂²⋊C₄	—	2	2	no	—
255	C₅×C₂²⋊C₄	—	4	2	no	—
256	C₅×C₂²⋊C₄	—	4	2	no	—
257	C₅×C₂²⋊C₄	—	4	2	no	—
258	C₄²×C₅	—	2	1	no	—
259	C₄²×C₅	—	2	1	no	—
260	C₄²×C₅	—	2	1	no	—
261	C₄²×C₅	—	2	1	no	—
262	C₄²×C₅	—	4	2	no	—
263	C₄²×C₅	—	4	2	no	—
264	C₄²×C₅	—	4	2	no	—
265	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
266	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
267	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
268	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
269	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
276	#462	—	2	4	no	—
277	#451	—	2	4	no	—
278	#451	—	2	4	no	—
279	#441	—	2	4	no	—
280	C₂×#106	C₂²×C₅	1	1	yes	characteristic
281	C₂×#106	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	C₂×#103	C₂²×C₅	1	1	yes	characteristic
284	C₂×#103	C₂²×C₅	1	1	yes	characteristic
285	C₂×#103	C₂²×C₅	1	1	yes	characteristic
286	C₂×#103	C₂²×C₅	1	1	yes	characteristic
287	C₂×#103	C₂²×C₅	1	1	yes	characteristic
288	C₂×#103	C₂²×C₅	1	1	yes	characteristic
289	C₂×#103	C₂²×C₅	1	1	yes	characteristic
290	C₂×#103	C₂²×C₅	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
293	C₂×#97	C₂²×C₅	1	1	yes	characteristic
294	#398	—	2	1	no	—
295	#396	—	2	1	no	—
296	#391	—	2	1	no	—
297	#391	—	2	1	no	—
298	#391	C₂²×C₅	1	1	yes	characteristic
299	#391	C₂²×C₅	1	1	yes	characteristic
300	#391	C₂²×C₅	1	1	yes	characteristic
301	#389	—	2	1	no	—
302	#389	C₂²×C₅	1	1	yes	characteristic
303	#388	—	2	1	no	—
304	#380	—	2	1	no	—
305	#380	C₂²×C₅	1	1	yes	characteristic
306	C₄×C₂²⋊C₄	—	2	1	no	—
307	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
308	#340	C₂²×C₅	1	1	yes	characteristic
309	#340	C₂²×C₅	1	1	yes	characteristic
310	#336	C₂²×C₅	1	1	yes	characteristic
311	#336	C₂²×C₅	1	1	yes	characteristic
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	#137	1	2	yes	—
319	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
320	C₅×Q₈	—	2	2	no	—
321	C₅×Q₈	—	2	2	no	—
322	C₅×Q₈	—	2	2	no	—
323	C₅×Q₈	—	2	2	no	—
324	C₅×Q₈	—	2	2	no	—
325	C₅×Q₈	—	2	2	no	—
326	C₅×Q₈	—	2	2	no	—
327	C₅×Q₈	—	4	8	no	—
328	C₅×Q₈	—	4	1	no	—
329	C₅×Q₈	—	4	1	no	—
330	C₅×Q₈	—	4	1	no	—
331	C₅×Q₈	—	4	1	no	—
332	C₅×Q₈	—	4	1	no	—
333	C₅×Q₈	—	4	1	no	—
334	C₅×Q₈	—	4	1	no	—
335	C₅×Q₈	—	4	1	no	—
336	C₅×Q₈	#121	1	4	yes	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	4	8	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	—	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	—	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	#137	1	2	yes	—
381	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
384	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
385	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
386	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
387	C₅×C₈	—	2	2	no	—
388	C₅×C₈	—	2	2	no	—
389	C₅×C₈	—	4	1	no	—
390	C₅×C₈	—	4	1	no	—
391	C₂²×Q₈	—	2	2	no	—
392	C₂²×Q₈	—	2	2	no	—
393	C₂²×Q₈	—	2	1	no	—
394	C₂²×Q₈	—	2	2	no	—
395	C₂²×Q₈	—	2	2	no	—
396	C₂²×Q₈	—	4	1	no	—
397	C₂²×Q₈	—	4	1	no	—
398	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
399	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
400	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂×Q₁₆	—	2	2	no	—
405	C₂×Q₁₆	—	2	2	no	—
406	C₂×Q₁₆	—	2	2	no	—
407	C₂×Q₁₆	—	2	2	no	—
408	C₂×Q₁₆	—	2	2	no	—
409	C₂×Q₁₆	—	2	2	no	—
410	C₂×Q₁₆	—	2	2	no	—
411	C₂×Q₁₆	—	2	2	no	—
412	C₂×Q₁₆	—	2	2	no	—
413	C₂×Q₁₆	—	4	1	no	—
414	C₂×Q₁₆	—	4	1	no	—
415	C₂×Q₁₆	C₅×D₄	1	4	yes	—
416	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
420	C₄⋊Q₈	—	2	2	no	—
421	C₄⋊Q₈	—	4	1	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	—	4	1	no	—
425	C₂²⋊Q₈	—	4	1	no	—
426	C₄×Q₈	—	2	2	no	—
427	C₄×Q₈	—	2	2	no	—
428	C₄×Q₈	—	2	2	no	—
429	C₄×Q₈	—	4	1	no	—
430	C₄×Q₈	—	4	1	no	—
431	C₄×Q₈	—	4	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	C₅×D₄	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
454	#106	—	2	2	no	—
455	#106	—	4	1	no	—
456	C₄⋊C₈	—	2	2	no	—
457	#103	—	2	2	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#103	—	2	2	no	—
461	#103	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	4	1	no	—
464	#103	C₅×D₄	1	4	yes	—
465	C₂²⋊C₈	—	2	2	no	—
466	C₂²⋊C₈	—	2	2	no	—
467	#97	—	2	2	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	C₅×D₄	1	1	yes	characteristic
477	#95	C₅×D₄	1	1	yes	characteristic
478	C₂²×C₅	—	2	2	no	—
479	C₂²×C₅	—	2	2	no	—
480	C₂²×C₅	—	2	2	no	—
481	C₂²×C₅	—	4	1	no	—
482	C₂²×C₅	—	4	1	no	—
483	C₂²×C₅	—	4	1	no	—
484	C₂²×C₅	—	4	1	no	—
485	C₂²×C₅	#525	1	1	yes	characteristic
486	C₂²×C₅	D₄²	1	1	yes	characteristic
487	C₂²×C₅	D₄²	1	1	yes	characteristic
488	C₂²×C₅	C₂×#137	1	1	yes	characteristic
489	C₂²×C₅	C₂×#137	1	1	yes	characteristic
490	C₂²×C₅	#578	1	1	yes	characteristic
491	C₂²×C₅	#578	1	1	yes	characteristic
492	C₄×C₅	—	2	4	no	—
493	C₄×C₅	—	2	2	no	—
494	C₄×C₅	—	4	1	no	—
495	C₄×C₅	—	4	2	no	—
496	C₄×C₅	—	4	2	no	—
497	C₄×C₅	—	4	1	no	—
498	C₄×C₅	—	4	1	no	—
499	C₄×C₅	—	4	1	no	—
500	C₄×C₅	—	4	2	no	—
501	C₄×C₅	—	8	1	no	—
502	C₄×C₅	—	8	1	no	—
503	C₄×C₅	—	8	1	no	—
504	C₄×C₅	—	8	1	no	—
505	C₄×C₅	C₂×#121	1	1	yes	characteristic
506	C₄×C₅	#538	1	1	yes	characteristic
507	C₄×C₅	#546	1	1	yes	characteristic
508	C₄×C₅	#546	1	1	yes	characteristic
509	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
510	C₂×Q₈	—	2	4	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	4	2	no	—
531	C₂×Q₈	—	4	2	no	—
532	C₂×Q₈	—	4	4	no	—
533	C₂×Q₈	—	4	4	no	—
534	C₂×Q₈	—	4	4	no	—
535	C₂×Q₈	—	4	4	no	—
536	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
537	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
538	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
539	C₂×Q₈	C₅×#41	1	2	yes	—
540	C₂×Q₈	C₅×#41	1	2	yes	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
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	—	2	1	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
559	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
560	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
561	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
562	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
564	Q₁₆	—	2	8	no	—
565	Q₁₆	—	4	4	no	—
566	Q₁₆	—	4	4	no	—
567	Q₁₆	—	4	4	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
579	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	2	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	4	2	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	4	2	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	4	2	no	—
606	C₄²	—	4	2	no	—
607	C₄²	—	4	2	no	—
608	C₂×C₅	—	4	2	no	—
609	C₂×C₅	#2424	1	1	yes	characteristic
610	C₂×C₅	#3113	1	1	yes	characteristic
611	C₂×C₅	#3127	1	1	yes	characteristic
612	C₂×C₅	#3270	1	1	yes	characteristic
613	C₂×C₅	#3270	1	1	yes	characteristic
614	C₂×C₅	#3270	1	1	yes	characteristic
615	C₂×C₅	#3276	1	1	yes	characteristic
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	C₅×#137	1	2	yes	—
623	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
624	Q₈	—	2	2	no	—
625	Q₈	—	2	2	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	4	8	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	Q₈	—	4	1	no	—
638	Q₈	—	4	1	no	—
639	Q₈	—	4	1	no	—
640	Q₈	C₅×#121	1	4	yes	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	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	2	no	—
652	C₂×C₄	—	2	2	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	—	4	8	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	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	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	C₅×#137	1	2	yes	—
685	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
686	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
687	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
688	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
689	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
690	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	2	no	—
693	C₈	—	4	1	no	—
694	C₈	—	4	1	no	—
695	C₅	#25173	1	1	yes	characteristic, direct product factor, Sylow
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	C₅×#525	1	1	yes	characteristic
704	C₂²	C₅×D₄²	1	1	yes	characteristic
705	C₂²	C₅×D₄²	1	1	yes	characteristic
706	C₂²	C₂×C₅×#137	1	1	yes	characteristic
707	C₂²	C₂×C₅×#137	1	1	yes	characteristic
708	C₂²	C₅×#578	1	1	yes	characteristic
709	C₂²	C₅×#578	1	1	yes	characteristic
710	C₄	—	2	2	no	—
711	C₄	—	2	4	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	8	1	no	—
720	C₄	—	8	1	no	—
721	C₄	—	8	1	no	—
722	C₄	—	8	1	no	—
723	C₄	C₂×C₅×#121	1	1	yes	characteristic
724	C₄	C₅×#538	1	1	yes	characteristic
725	C₄	C₅×#546	1	1	yes	characteristic
726	C₄	C₅×#546	1	1	yes	characteristic
727	C₂	—	4	2	no	—
728	C₂	C₅×#2424	1	1	yes	characteristic
729	C₂	C₅×#3113	1	1	yes	characteristic
730	C₂	C₅×#3127	1	1	yes	characteristic
731	C₂	C₅×#3270	1	1	yes	characteristic
732	C₂	C₅×#3270	1	1	yes	characteristic
733	C₂	C₅×#3270	1	1	yes	characteristic
734	C₂	C₅×#3276	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
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×#462	C₂	semidirect
4. C₂×C₅×#441	C₂	semidirect
7. C₅×#2066	C₂	semidirect
10. C₅×#2016	C₂	semidirect
11. C₅×#1971	C₂	semidirect
13. C₅×#1878	C₂	semidirect
14. C₅×#1878	C₂	semidirect
15. C₅×#1865	C₂	semidirect
63. #25173	C₅	direct (N × H)
151. C₂×#462	C₂×C₅	semidirect
154. C₂×#441	C₂×C₅	semidirect
157. #2066	C₂×C₅	semidirect
160. #2016	C₂×C₅	semidirect
161. #1971	C₂×C₅	semidirect
163. #1878	C₂×C₅	semidirect
164. #1878	C₂×C₅	semidirect
165. #1865	C₂×C₅	semidirect
695. C₅	#25173	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×#462	2
C₂×C₅×#451	2
C₂×C₅×#441	2
C₅×#2429	2
C₅×Q₈×C₂²⋊C₄	2
C₅×#2066	2
C₅×#2035	2
C₅×#2016	2
C₅×#1971	2
C₅×#1924	2
C₅×#1878	2
C₅×#1865	2
#25173	5

Subgroups — C5×#25173 #11947893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25173 #11947893