Subgroups — C₅×#22233 #11944953

Order 1280.

782 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#489	C₂	1	1	yes	maximal, characteristic
2	C₅×#2331	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2326	C₂	1	1	yes	maximal, characteristic
4	C₅×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1958	C₂	1	1	yes	maximal, characteristic
6	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1927	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1926	C₂	1	1	yes	maximal, characteristic
9	C₅×#1925	C₂	1	1	yes	maximal, characteristic
10	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1864	C₂	1	1	yes	maximal, characteristic
12	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1862	C₂	1	1	yes	maximal, characteristic
14	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#124	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₅×#489	C₄	1	8	yes	complemented
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
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×#103	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×#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
33	C₂×C₅×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#391	—	2	1	no	—
36	C₅×#391	—	2	1	no	—
37	C₅×#391	C₂²	1	1	yes	characteristic
38	C₅×#390	C₂²	1	1	yes	characteristic
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#389	C₂²	1	1	yes	characteristic
41	C₅×#388	—	2	1	no	—
42	C₅×#388	—	2	1	no	—
43	C₅×#387	—	2	1	no	—
44	C₅×#387	—	2	1	no	—
45	C₅×#385	—	2	1	no	—
46	C₅×#385	—	2	1	no	—
47	C₅×#384	C₂²	1	1	yes	characteristic
48	C₅×#382	C₂²	1	1	yes	characteristic
49	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₅×#376	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×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	#22233	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	—	2	1	no	—
62	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₅	—	2	1	no	—
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₅×C₄⋊Q₈	—	2	2	no	—
70	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
71	C₅×#124	—	2	2	no	—
72	C₅×#124	C₂×C₄	1	4	yes	—
73	C₄×C₅×Q₈	—	4	1	no	—
74	C₄×C₅×Q₈	—	4	1	no	—
75	C₄×C₅×D₄	—	4	1	no	—
76	C₄×C₅×D₄	—	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	1	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	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₄²×C₅	—	2	1	no	—
95	C₂×C₄²×C₅	—	2	1	no	—
96	C₂×C₄²×C₅	—	2	1	no	—
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×#107	—	4	1	no	—
101	C₅×#107	—	4	1	no	—
102	C₅×#106	—	4	1	no	—
103	C₅×#106	—	4	1	no	—
104	C₅×#103	—	4	1	no	—
105	C₅×#103	—	4	1	no	—
106	C₅×#103	C₂×C₄	1	4	yes	complemented
107	C₅×#103	C₂×C₄	1	4	yes	complemented
108	C₅×#102	—	4	1	no	—
109	C₅×#102	—	4	1	no	—
110	C₅×#102	C₂×C₄	1	4	yes	—
111	C₅×#102	C₂×C₄	1	4	yes	—
112	C₅×#97	C₂×C₄	1	4	yes	complemented
113	C₄×C₅×C₈	—	2	2	no	—
114	C₅×#95	—	2	1	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	D₄	1	1	yes	characteristic
123	C₅×#95	D₄	1	1	yes	characteristic
124	C₅×#95	D₄	1	1	yes	characteristic
125	C₅×#95	D₄	1	1	yes	characteristic
126	C₂×#489	C₂×C₅	1	1	yes	characteristic
127	#2331	C₂×C₅	1	1	yes	characteristic, complemented
128	#2326	C₂×C₅	1	1	yes	characteristic
129	#1990	C₂×C₅	1	1	yes	characteristic, complemented
130	#1958	C₂×C₅	1	1	yes	characteristic
131	#1928	C₂×C₅	1	1	yes	characteristic, complemented
132	#1927	C₂×C₅	1	1	yes	characteristic, complemented
133	#1926	C₂×C₅	1	1	yes	characteristic
134	#1925	C₂×C₅	1	1	yes	characteristic
135	#1865	C₂×C₅	1	1	yes	characteristic, complemented
136	#1864	C₂×C₅	1	1	yes	characteristic
137	#1863	C₂×C₅	1	1	yes	characteristic, complemented
138	#1862	C₂×C₅	1	1	yes	characteristic
139	#1847	C₂×C₅	1	1	yes	characteristic, complemented
140	#1746	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂⁴×C₅	—	2	1	no	—
142	C₂×C₅×Q₈	—	2	4	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	—	2	1	no	—
148	C₂×C₅×Q₈	—	8	1	no	—
149	C₂×C₅×Q₈	—	8	1	no	—
150	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	2	1	no	—
154	C₂×C₅×D₄	—	2	1	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₅	—	2	1	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	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	4	2	no	—
165	C₂²×C₄×C₅	—	8	1	no	—
166	C₂²×C₄×C₅	—	8	1	no	—
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
185	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
186	C₅×C₄⋊C₄	—	2	4	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	—	2	1	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	—	8	1	no	—
201	C₅×C₄⋊C₄	—	8	1	no	—
202	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
203	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
204	C₅×C₂²⋊C₄	—	2	4	no	—
205	C₅×C₂²⋊C₄	—	2	4	no	—
206	C₅×C₂²⋊C₄	—	4	2	no	—
207	C₅×C₂²⋊C₄	—	8	1	no	—
208	C₅×C₂²⋊C₄	—	8	1	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	—	8	1	no	—
215	C₄²×C₅	—	8	1	no	—
216	C₄²×C₅	C₂²×C₄	1	2	yes	—
217	C₄²×C₅	#41	1	2	yes	—
218	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
219	C₂×#124	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
222	#489	C₄×C₅	1	8	yes	complemented
223	C₂×#107	C₂²×C₅	1	1	yes	characteristic
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×#103	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×#102	C₂²×C₅	1	1	yes	characteristic
232	C₂×#102	C₂²×C₅	1	1	yes	characteristic
233	C₂×#102	C₂²×C₅	1	1	yes	characteristic
234	C₂×#102	C₂²×C₅	1	1	yes	characteristic
235	C₂×#97	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
237	#391	—	2	1	no	—
238	#391	—	2	1	no	—
239	#391	C₂²×C₅	1	1	yes	characteristic
240	#390	C₂²×C₅	1	1	yes	characteristic
241	#389	C₂²×C₅	1	1	yes	characteristic
242	#389	C₂²×C₅	1	1	yes	characteristic
243	#388	—	2	1	no	—
244	#388	—	2	1	no	—
245	#387	—	2	1	no	—
246	#387	—	2	1	no	—
247	#385	—	2	1	no	—
248	#385	—	2	1	no	—
249	#384	C₂²×C₅	1	1	yes	characteristic
250	#382	C₂²×C₅	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	#376	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	#336	C₂²×C₅	1	1	yes	characteristic
259	#336	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	2	no	—
263	C₂³×C₅	—	4	1	no	—
264	C₂³×C₅	—	4	1	no	—
265	C₂³×C₅	—	4	1	no	—
266	C₂³×C₅	—	4	1	no	—
267	C₂³×C₅	—	4	1	no	—
268	C₂³×C₅	—	4	1	no	—
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	C₅×Q₈	—	8	4	no	—
275	C₅×D₄	—	2	2	no	—
276	C₅×D₄	—	2	2	no	—
277	C₅×D₄	—	4	1	no	—
278	C₅×D₄	—	4	1	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	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	1	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	—	2	1	no	—
297	C₂×C₄×C₅	—	2	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	—	4	1	no	—
316	C₂×C₄×C₅	—	8	4	no	—
317	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
318	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
319	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₅	H(5,𝔽₂)	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	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
325	C₅×C₈	—	2	2	no	—
326	C₅×C₈	—	2	2	no	—
327	C₅×C₈	—	4	1	no	—
328	C₅×C₈	—	4	1	no	—
329	C₂²×Q₈	—	2	1	no	—
330	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
339	#124	—	2	2	no	—
340	#124	C₂×C₄×C₅	1	4	yes	—
341	C₄×Q₈	—	4	1	no	—
342	C₄×Q₈	—	4	1	no	—
343	C₄×D₄	—	4	1	no	—
344	C₄×D₄	—	4	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	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	C₂³×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
368	#107	—	4	1	no	—
369	#107	—	4	1	no	—
370	#106	—	4	1	no	—
371	#106	—	4	1	no	—
372	#103	—	4	1	no	—
373	#103	—	4	1	no	—
374	#103	C₂×C₄×C₅	1	4	yes	complemented
375	#103	C₂×C₄×C₅	1	4	yes	complemented
376	#102	—	4	1	no	—
377	#102	—	4	1	no	—
378	#102	C₂×C₄×C₅	1	4	yes	—
379	#102	C₂×C₄×C₅	1	4	yes	—
380	#97	C₂×C₄×C₅	1	4	yes	complemented
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	C₅×D₄	1	1	yes	characteristic
391	#95	C₅×D₄	1	1	yes	characteristic
392	#95	C₅×D₄	1	1	yes	characteristic
393	#95	C₅×D₄	1	1	yes	characteristic
394	C₂²×C₅	—	4	2	no	—
395	C₂²×C₅	—	4	2	no	—
396	C₂²×C₅	—	4	2	no	—
397	C₂²×C₅	—	8	1	no	—
398	C₂²×C₅	—	8	1	no	—
399	C₂²×C₅	—	8	1	no	—
400	C₂²×C₅	—	8	1	no	—
401	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
402	C₂²×C₅	#535	1	1	yes	characteristic
403	C₂²×C₅	#536	1	1	yes	characteristic
404	C₂²×C₅	#576	1	1	yes	characteristic
405	C₂²×C₅	#577	1	1	yes	characteristic
406	C₂²×C₅	#577	1	1	yes	characteristic
407	C₂²×C₅	#578	1	1	yes	characteristic
408	C₄×C₅	—	2	2	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	4	2	no	—
411	C₄×C₅	—	4	2	no	—
412	C₄×C₅	—	4	2	no	—
413	C₄×C₅	—	4	1	no	—
414	C₄×C₅	—	4	1	no	—
415	C₄×C₅	—	4	1	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	—	8	1	no	—
421	C₄×C₅	#520	1	1	yes	characteristic
422	C₄×C₅	#520	1	1	yes	characteristic
423	C₄×C₅	#542	1	1	yes	characteristic
424	C₄×C₅	#542	1	1	yes	characteristic
425	C₂⁴	—	2	1	no	—
426	C₂×Q₈	—	2	4	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	8	1	no	—
433	C₂×Q₈	—	8	1	no	—
434	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	8	1	no	—
450	C₂²×C₄	—	8	1	no	—
451	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
452	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
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	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
469	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
470	C₄⋊C₄	—	2	4	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	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₄⋊C₄	—	8	1	no	—
483	C₄⋊C₄	—	8	1	no	—
484	C₄⋊C₄	—	8	1	no	—
485	C₄⋊C₄	—	8	1	no	—
486	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
487	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₂²⋊C₄	—	8	1	no	—
492	C₂²⋊C₄	—	8	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	4	2	no	—
498	C₄²	—	8	1	no	—
499	C₄²	—	8	1	no	—
500	C₄²	C₂²×C₄×C₅	1	2	yes	—
501	C₄²	C₅×#41	1	2	yes	—
502	C₂×C₅	—	8	2	no	—
503	C₂×C₅	#2326	1	1	yes	characteristic
504	C₂×C₅	#2946	1	1	yes	characteristic
505	C₂×C₅	#2947	1	1	yes	characteristic
506	C₂×C₅	#3224	1	1	yes	characteristic
507	C₂×C₅	#3225	1	1	yes	characteristic
508	C₂×C₅	#3243	1	1	yes	characteristic
509	C₂×C₅	#3244	1	1	yes	characteristic
510	C₂³	—	2	2	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	8	4	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	2	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	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	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	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	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	8	4	no	—
565	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
566	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
567	C₂×C₄	C₂³×C₄×C₅	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×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
572	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
573	C₈	—	2	2	no	—
574	C₈	—	2	2	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₅	#22233	1	1	yes	characteristic, direct product factor, Sylow
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	8	1	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
586	C₂²	C₅×#535	1	1	yes	characteristic
587	C₂²	C₅×#536	1	1	yes	characteristic
588	C₂²	C₅×#576	1	1	yes	characteristic
589	C₂²	C₅×#577	1	1	yes	characteristic
590	C₂²	C₅×#577	1	1	yes	characteristic
591	C₂²	C₅×#578	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	C₅×#520	1	1	yes	characteristic
606	C₄	C₅×#520	1	1	yes	characteristic
607	C₄	C₅×#542	1	1	yes	characteristic
608	C₄	C₅×#542	1	1	yes	characteristic
609	C₂	—	8	2	no	—
610	C₂	C₅×#2326	1	1	yes	characteristic
611	C₂	C₅×#2946	1	1	yes	characteristic
612	C₂	C₅×#2947	1	1	yes	characteristic
613	C₂	C₅×#3224	1	1	yes	characteristic
614	C₂	C₅×#3225	1	1	yes	characteristic
615	C₂	C₅×#3243	1	1	yes	characteristic
616	C₂	C₅×#3244	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	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2331	C₂	semidirect
4. C₅×#1990	C₂	semidirect
6. C₅×#1928	C₂	semidirect
7. C₅×#1927	C₂	semidirect
10. C₅×#1865	C₂	semidirect
12. C₅×#1863	C₂	semidirect
14. C₅×#1847	C₂	semidirect
15. C₅×#1746	C₂	semidirect
20. C₅×#489	C₄	semidirect
60. #22233	C₅	direct (N × H)
70. C₅×C₄⋊Q₈	C₂×C₄	semidirect
106. C₅×#103	C₂×C₄	semidirect
107. C₅×#103	C₂×C₄	semidirect
112. C₅×#97	C₂×C₄	semidirect
127. #2331	C₂×C₅	semidirect
129. #1990	C₂×C₅	semidirect
131. #1928	C₂×C₅	semidirect
132. #1927	C₂×C₅	semidirect
135. #1865	C₂×C₅	semidirect
137. #1863	C₂×C₅	semidirect
139. #1847	C₂×C₅	semidirect
140. #1746	C₂×C₅	semidirect
222. #489	C₄×C₅	semidirect
338. C₄⋊Q₈	C₂×C₄×C₅	semidirect
374. #103	C₂×C₄×C₅	semidirect
375. #103	C₂×C₄×C₅	semidirect
380. #97	C₂×C₄×C₅	semidirect
577. C₅	#22233	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×#489	2
C₅×#2331	2
C₅×#2326	2
C₅×#1990	2
C₅×#1958	2
C₅×#1928	2
C₅×#1927	2
C₅×#1926	2
C₅×#1925	2
C₅×#1865	2
C₅×#1864	2
C₅×#1863	2
C₅×#1862	2
C₅×#1847	2
C₅×#1746	2
#22233	5

Subgroups — C5×#22233 #11944953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22233 #11944953