Subgroups — C₅×#22945 #11945665

Order 1280.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#483	C₂	1	1	yes	maximal, characteristic
2	C₅×#2362	C₂	1	1	yes	maximal, characteristic
3	C₅×#2345	C₂	1	1	yes	maximal, characteristic
4	C₅×#1944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1920	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1894	C₂	1	1	yes	maximal, characteristic
10	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1854	C₂	1	1	yes	maximal, characteristic
12	C₄×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1753	C₂	1	1	yes	maximal, characteristic
15	C₅×#1736	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₅×#483	C₄	1	8	yes	complemented
22	C₂×C₅×#107	C₂²	1	1	yes	characteristic
23	C₂×C₅×#106	C₂²	1	1	yes	characteristic
24	C₂×C₅×#106	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×#103	C₂²	1	1	yes	characteristic
27	C₂×C₅×#103	C₂²	1	1	yes	characteristic
28	C₂×C₅×#103	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#391	C₂²	1	1	yes	characteristic
34	C₅×#389	C₂²	1	1	yes	characteristic
35	C₅×#389	C₂²	1	1	yes	characteristic
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#388	—	2	1	no	—
38	C₅×#388	—	2	1	no	—
39	C₅×#387	—	2	1	no	—
40	C₅×#387	—	2	1	no	—
41	C₅×#387	—	2	1	no	—
42	C₅×#380	—	2	1	no	—
43	C₅×#380	C₂²	1	1	yes	characteristic
44	C₄×C₅×C₄⋊C₄	—	2	1	no	—
45	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₅×#340	C₂²	1	1	yes	characteristic
51	C₅×#340	C₂²	1	1	yes	characteristic
52	C₅×#340	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	#22945	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₅	—	2	1	no	—
63	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₅×M₁₆	—	2	2	no	—
65	C₂×C₅×M₁₆	—	2	2	no	—
66	C₂×C₅×M₁₆	—	4	1	no	—
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₅×C₂²⋊Q₈	—	2	2	no	—
72	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
73	C₄×C₅×Q₈	—	2	2	no	—
74	C₄×C₅×Q₈	—	4	1	no	—
75	C₅×#117	—	2	2	no	—
76	C₅×#117	—	4	1	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	2	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	—	2	1	no	—
98	C₂×C₄²×C₅	—	2	1	no	—
99	C₂×C₄²×C₅	—	2	1	no	—
100	C₂×C₄²×C₅	—	2	1	no	—
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₅×#107	—	4	1	no	—
105	C₅×#106	—	2	2	no	—
106	C₅×#106	C₂×C₄	1	4	yes	—
107	C₅×#106	C₂×C₄	1	4	yes	—
108	C₅×#103	—	2	2	no	—
109	C₅×#103	—	4	1	no	—
110	C₅×#103	C₂×C₄	1	4	yes	—
111	C₅×#103	C₂×C₄	1	4	yes	—
112	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
113	C₅×#97	—	4	1	no	—
114	C₄×C₅×C₈	—	2	2	no	—
115	C₅×#95	—	2	1	no	—
116	C₅×#95	—	2	1	no	—
117	C₅×#95	—	2	1	no	—
118	C₅×#95	—	2	1	no	—
119	C₅×#95	—	2	1	no	—
120	C₅×#95	—	2	1	no	—
121	C₅×#95	—	2	1	no	—
122	C₅×#95	—	2	1	no	—
123	C₅×#95	—	2	1	no	—
124	C₅×#95	D₄	1	1	yes	characteristic
125	C₅×#95	D₄	1	1	yes	characteristic
126	C₂×#483	C₂×C₅	1	1	yes	characteristic
127	#2362	C₂×C₅	1	1	yes	characteristic
128	#2345	C₂×C₅	1	1	yes	characteristic
129	#1944	C₂×C₅	1	1	yes	characteristic, complemented
130	#1933	C₂×C₅	1	1	yes	characteristic, complemented
131	#1928	C₂×C₅	1	1	yes	characteristic, complemented
132	#1920	C₂×C₅	1	1	yes	characteristic, complemented
133	#1920	C₂×C₅	1	1	yes	characteristic, complemented
134	#1894	C₂×C₅	1	1	yes	characteristic
135	#1865	C₂×C₅	1	1	yes	characteristic, complemented
136	#1854	C₂×C₅	1	1	yes	characteristic
137	C₄×#106	C₂×C₅	1	1	yes	characteristic, complemented
138	#1763	C₂×C₅	1	1	yes	characteristic, complemented
139	#1753	C₂×C₅	1	1	yes	characteristic
140	#1736	C₂×C₅	1	1	yes	characteristic
141	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×Q₈	—	2	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	—	2	1	no	—
147	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	4	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	8	1	no	—
162	C₂²×C₄×C₅	—	8	1	no	—
163	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	#41	1	2	yes	—
170	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
171	C₅×M₁₆	—	4	4	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
182	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
183	C₂×C₅×C₈	#41	1	2	yes	—
184	C₅×C₄⋊C₄	—	2	4	no	—
185	C₅×C₄⋊C₄	—	2	4	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	4	2	no	—
197	C₅×C₄⋊C₄	—	4	2	no	—
198	C₅×C₄⋊C₄	—	8	1	no	—
199	C₅×C₄⋊C₄	—	8	1	no	—
200	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
201	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
202	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
203	C₅×C₄⋊C₄	#41	1	2	yes	—
204	C₅×C₂²⋊C₄	—	2	4	no	—
205	C₅×C₂²⋊C₄	—	2	2	no	—
206	C₅×C₂²⋊C₄	—	4	1	no	—
207	C₅×C₂²⋊C₄	—	4	2	no	—
208	C₅×C₂²⋊C₄	—	4	2	no	—
209	C₄²×C₅	—	2	1	no	—
210	C₄²×C₅	—	2	1	no	—
211	C₄²×C₅	—	2	1	no	—
212	C₄²×C₅	—	2	1	no	—
213	C₄²×C₅	—	4	2	no	—
214	C₄²×C₅	—	4	2	no	—
215	C₄²×C₅	—	4	2	no	—
216	C₄²×C₅	—	8	1	no	—
217	C₄²×C₅	—	8	1	no	—
218	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×#117	C₂²×C₅	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
223	#483	C₄×C₅	1	8	yes	complemented
224	C₂×#107	C₂²×C₅	1	1	yes	characteristic
225	C₂×#106	C₂²×C₅	1	1	yes	characteristic
226	C₂×#106	C₂²×C₅	1	1	yes	characteristic
227	C₂×#106	C₂²×C₅	1	1	yes	characteristic
228	C₂×#103	C₂²×C₅	1	1	yes	characteristic
229	C₂×#103	C₂²×C₅	1	1	yes	characteristic
230	C₂×#103	C₂²×C₅	1	1	yes	characteristic
231	C₂×#103	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
233	C₂×#97	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
235	#391	C₂²×C₅	1	1	yes	characteristic
236	#389	C₂²×C₅	1	1	yes	characteristic
237	#389	C₂²×C₅	1	1	yes	characteristic
238	#389	C₂²×C₅	1	1	yes	characteristic
239	#388	—	2	1	no	—
240	#388	—	2	1	no	—
241	#387	—	2	1	no	—
242	#387	—	2	1	no	—
243	#387	—	2	1	no	—
244	#380	—	2	1	no	—
245	#380	C₂²×C₅	1	1	yes	characteristic
246	C₄×C₄⋊C₄	—	2	1	no	—
247	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₄×C₂²⋊C₄	—	2	1	no	—
251	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	#340	C₂²×C₅	1	1	yes	characteristic
253	#340	C₂²×C₅	1	1	yes	characteristic
254	#340	C₂²×C₅	1	1	yes	characteristic
255	#340	C₂²×C₅	1	1	yes	characteristic
256	#340	C₂²×C₅	1	1	yes	characteristic
257	#340	C₂²×C₅	1	1	yes	characteristic
258	#340	C₂²×C₅	1	1	yes	characteristic
259	#340	C₂²×C₅	1	1	yes	characteristic
260	#336	C₂²×C₅	1	1	yes	characteristic
261	#336	C₂²×C₅	1	1	yes	characteristic
262	C₂³×C₅	—	2	1	no	—
263	C₂³×C₅	—	2	1	no	—
264	C₂³×C₅	—	2	1	no	—
265	C₂³×C₅	—	2	1	no	—
266	C₂³×C₅	—	2	1	no	—
267	C₂³×C₅	—	2	1	no	—
268	C₂³×C₅	C₄×D₄	1	2	yes	—
269	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₅×Q₈	—	2	2	no	—
271	C₅×Q₈	—	2	2	no	—
272	C₅×Q₈	—	4	1	no	—
273	C₅×Q₈	—	4	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	4	1	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	8	4	no	—
316	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
317	C₂×C₄×C₅	#137	1	2	yes	—
318	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
324	C₅×C₈	—	2	2	no	—
325	C₅×C₈	—	2	2	no	—
326	C₅×C₈	—	2	2	no	—
327	C₅×C₈	—	4	1	no	—
328	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	4	1	no	—
334	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	—	4	1	no	—
342	#117	—	2	2	no	—
343	#117	—	4	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
352	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
371	#107	—	4	1	no	—
372	#106	—	2	2	no	—
373	#106	C₂×C₄×C₅	1	4	yes	—
374	#106	C₂×C₄×C₅	1	4	yes	—
375	#103	—	2	2	no	—
376	#103	—	4	1	no	—
377	#103	C₂×C₄×C₅	1	4	yes	—
378	#103	C₂×C₄×C₅	1	4	yes	—
379	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
380	#97	—	4	1	no	—
381	C₄×C₈	—	2	2	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	C₅×D₄	1	1	yes	characteristic
392	#95	C₅×D₄	1	1	yes	characteristic
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	—	2	2	no	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	4	1	no	—
397	C₂²×C₅	—	4	1	no	—
398	C₂²×C₅	—	4	1	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
401	C₂²×C₅	#546	1	1	yes	characteristic
402	C₂²×C₅	#547	1	1	yes	characteristic
403	C₂²×C₅	C₂×#137	1	1	yes	characteristic
404	C₂²×C₅	#575	1	1	yes	characteristic
405	C₂²×C₅	#577	1	1	yes	characteristic
406	C₂²×C₅	#577	1	1	yes	characteristic
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	2	2	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	4	2	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	2	no	—
413	C₄×C₅	—	4	2	no	—
414	C₄×C₅	—	4	2	no	—
415	C₄×C₅	—	4	2	no	—
416	C₄×C₅	—	4	1	no	—
417	C₄×C₅	—	8	1	no	—
418	C₄×C₅	—	8	1	no	—
419	C₄×C₅	—	8	1	no	—
420	C₄×C₅	C₄×#41	1	1	yes	characteristic
421	C₄×C₅	#520	1	1	yes	characteristic
422	C₄×C₅	#551	1	1	yes	characteristic
423	C₄×C₅	#552	1	1	yes	characteristic
424	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	8	1	no	—
445	C₂²×C₄	—	8	1	no	—
446	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
447	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
452	C₂²×C₄	C₅×#41	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
454	M₁₆	—	4	4	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
465	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
466	C₂×C₈	C₅×#41	1	2	yes	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	4	2	no	—
480	C₄⋊C₄	—	4	2	no	—
481	C₄⋊C₄	—	8	1	no	—
482	C₄⋊C₄	—	8	1	no	—
483	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
484	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
485	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
486	C₄⋊C₄	C₅×#41	1	2	yes	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₂²⋊C₄	—	4	2	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	4	2	no	—
497	C₄²	—	4	2	no	—
498	C₄²	—	4	2	no	—
499	C₄²	—	8	1	no	—
500	C₄²	—	8	1	no	—
501	C₂×C₅	—	4	2	no	—
502	C₂×C₅	#2359	1	1	yes	characteristic
503	C₂×C₅	C₄×#137	1	1	yes	characteristic
504	C₂×C₅	#2949	1	1	yes	characteristic
505	C₂×C₅	#3326	1	1	yes	characteristic
506	C₂×C₅	#3331	1	1	yes	characteristic
507	C₂×C₅	#3344	1	1	yes	characteristic
508	C₂×C₅	#3350	1	1	yes	characteristic
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	C₄×C₅×D₄	1	2	yes	—
516	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	8	4	no	—
563	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
564	C₂×C₄	C₅×#137	1	2	yes	—
565	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
566	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
567	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
568	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
569	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
571	C₈	—	2	2	no	—
572	C₈	—	2	2	no	—
573	C₈	—	2	2	no	—
574	C₈	—	4	1	no	—
575	C₅	#22945	1	1	yes	characteristic, direct product factor, Sylow
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
584	C₂²	C₅×#546	1	1	yes	characteristic
585	C₂²	C₅×#547	1	1	yes	characteristic
586	C₂²	C₂×C₅×#137	1	1	yes	characteristic
587	C₂²	C₅×#575	1	1	yes	characteristic
588	C₂²	C₅×#577	1	1	yes	characteristic
589	C₂²	C₅×#577	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	8	1	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	C₄×C₅×#41	1	1	yes	characteristic
604	C₄	C₅×#520	1	1	yes	characteristic
605	C₄	C₅×#551	1	1	yes	characteristic
606	C₄	C₅×#552	1	1	yes	characteristic
607	C₂	—	4	2	no	—
608	C₂	C₅×#2359	1	1	yes	characteristic
609	C₂	C₄×C₅×#137	1	1	yes	characteristic
610	C₂	C₅×#2949	1	1	yes	characteristic
611	C₂	C₅×#3326	1	1	yes	characteristic
612	C₂	C₅×#3331	1	1	yes	characteristic
613	C₂	C₅×#3344	1	1	yes	characteristic
614	C₂	C₅×#3350	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	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×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
4. C₅×#1944	C₂	semidirect
5. C₅×#1933	C₂	semidirect
6. C₅×#1928	C₂	semidirect
7. C₅×#1920	C₂	semidirect
8. C₅×#1920	C₂	semidirect
10. C₅×#1865	C₂	semidirect
12. C₄×C₅×#106	C₂	semidirect
13. C₅×#1763	C₂	semidirect
21. C₅×#483	C₄	semidirect
60. #22945	C₅	direct (N × H)
129. #1944	C₂×C₅	semidirect
130. #1933	C₂×C₅	semidirect
131. #1928	C₂×C₅	semidirect
132. #1920	C₂×C₅	semidirect
133. #1920	C₂×C₅	semidirect
135. #1865	C₂×C₅	semidirect
137. C₄×#106	C₂×C₅	semidirect
138. #1763	C₂×C₅	semidirect
223. #483	C₄×C₅	semidirect
575. C₅	#22945	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×#483	2
C₅×#2362	2
C₅×#2345	2
C₅×#1944	2
C₅×#1933	2
C₅×#1928	2
C₅×#1920	2
C₅×#1894	2
C₅×#1865	2
C₅×#1854	2
C₄×C₅×#106	2
C₅×#1763	2
C₅×#1753	2
C₅×#1736	2
#22945	5

Subgroups — C5×#22945 #11945665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22945 #11945665