Subgroups — C₅×#25995 #11948715

Order 1280.

702 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2439	C₂	1	1	yes	maximal, characteristic
2	C₅×#2346	C₂	1	1	yes	maximal, characteristic
3	C₅×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2088	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1918	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1854	C₂	1	1	yes	maximal, characteristic
12	C₅×#1850	C₂	1	1	yes	maximal, characteristic
13	C₅×#1825	C₂	1	1	yes	maximal, characteristic
14	C₅×#1808	C₂	1	1	yes	maximal, characteristic
15	C₅×#1735	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#117	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₅×#107	C₂²	1	1	yes	characteristic
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×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₅×#396	—	2	1	no	—
28	C₅×#393	—	2	1	no	—
29	C₅×#391	—	2	1	no	—
30	C₅×#389	C₂²	1	1	yes	characteristic
31	C₅×#389	C₂²	1	1	yes	characteristic
32	C₅×#389	C₂²	1	1	yes	characteristic
33	C₅×#389	C₂²	1	1	yes	characteristic
34	C₅×#388	—	2	1	no	—
35	C₅×#388	—	2	1	no	—
36	C₅×#387	—	2	1	no	—
37	C₅×#382	—	2	1	no	—
38	C₅×#382	C₂²	1	1	yes	characteristic
39	C₅×#380	C₂²	1	1	yes	characteristic
40	C₅×#380	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₅×#376	—	2	1	no	—
45	C₅×#340	C₂²	1	1	yes	characteristic
46	C₅×#340	C₂²	1	1	yes	characteristic
47	C₅×#340	C₂²	1	1	yes	characteristic
48	C₅×#340	C₂²	1	1	yes	characteristic
49	C₅×#340	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×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#25995	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	—	2	1	no	—
61	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	—	2	2	no	—
63	C₂²×C₅×C₈	—	2	2	no	—
64	C₂²×C₅×C₈	—	4	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	—	4	1	no	—
71	C₅×#117	—	2	2	no	—
72	C₅×#117	—	2	2	no	—
73	C₅×#117	—	4	1	no	—
74	C₅×#117	Q₈	1	4	yes	complemented
75	C₂×C₅×C₄⋊C₄	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	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	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	—	2	1	no	—
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×#107	—	2	2	no	—
101	C₅×#107	—	2	2	no	—
102	C₅×#107	—	4	1	no	—
103	C₅×#106	—	4	1	no	—
104	C₅×C₄⋊C₈	—	2	2	no	—
105	C₅×C₄⋊C₈	—	4	1	no	—
106	C₅×C₂²⋊C₈	—	2	2	no	—
107	C₅×#95	—	2	1	no	—
108	C₅×#95	—	2	1	no	—
109	C₅×#95	—	2	1	no	—
110	C₅×#95	—	2	1	no	—
111	C₅×#95	—	2	1	no	—
112	C₅×#95	—	2	1	no	—
113	C₅×#95	—	2	1	no	—
114	C₅×#95	—	2	1	no	—
115	C₅×#95	—	2	1	no	—
116	C₅×#95	—	2	1	no	—
117	C₅×#95	D₄	1	1	yes	characteristic
118	C₅×#95	D₄	1	1	yes	characteristic
119	#2439	C₂×C₅	1	1	yes	characteristic
120	#2346	C₂×C₅	1	1	yes	characteristic
121	#2101	C₂×C₅	1	1	yes	characteristic, complemented
122	#2088	C₂×C₅	1	1	yes	characteristic, complemented
123	#2086	C₂×C₅	1	1	yes	characteristic, complemented
124	#2057	C₂×C₅	1	1	yes	characteristic, complemented
125	#1987	C₂×C₅	1	1	yes	characteristic, complemented
126	#1949	C₂×C₅	1	1	yes	characteristic, complemented
127	#1921	C₂×C₅	1	1	yes	characteristic, complemented
128	#1918	C₂×C₅	1	1	yes	characteristic, complemented
129	#1854	C₂×C₅	1	1	yes	characteristic
130	#1850	C₂×C₅	1	1	yes	characteristic
131	#1825	C₂×C₅	1	1	yes	characteristic
132	#1808	C₂×C₅	1	1	yes	characteristic
133	#1735	C₂×C₅	1	1	yes	characteristic
134	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅×Q₈	—	4	2	no	—
136	C₂×C₅×Q₈	—	4	2	no	—
137	C₂×C₅×Q₈	—	8	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
156	C₂²×C₄×C₅	#41	1	2	yes	—
157	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	4	4	no	—
170	C₂×C₅×C₈	#41	1	2	yes	—
171	C₅×C₄⋊C₄	—	2	1	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	—	2	1	no	—
176	C₅×C₄⋊C₄	—	2	1	no	—
177	C₅×C₄⋊C₄	—	2	1	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	1	no	—
182	C₅×C₄⋊C₄	—	2	1	no	—
183	C₅×C₄⋊C₄	—	2	1	no	—
184	C₅×C₄⋊C₄	—	4	2	no	—
185	C₅×C₄⋊C₄	—	4	2	no	—
186	C₅×C₄⋊C₄	—	8	1	no	—
187	C₅×C₄⋊C₄	—	8	1	no	—
188	C₅×C₄⋊C₄	—	8	1	no	—
189	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
190	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
191	C₅×C₄⋊C₄	#41	1	2	yes	—
192	C₅×C₂²⋊C₄	—	2	4	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	4	1	no	—
195	C₅×C₂²⋊C₄	—	4	2	no	—
196	C₅×C₂²⋊C₄	—	8	1	no	—
197	C₅×C₂²⋊C₄	—	8	1	no	—
198	C₄²×C₅	—	2	4	no	—
199	C₄²×C₅	—	2	1	no	—
200	C₄²×C₅	—	2	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	—	4	2	no	—
204	C₄²×C₅	—	4	2	no	—
205	C₄²×C₅	—	4	2	no	—
206	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
208	C₂×#117	C₂²×C₅	1	1	yes	characteristic
209	C₂×#117	C₂²×C₅	1	1	yes	characteristic
210	C₂×#107	C₂²×C₅	1	1	yes	characteristic
211	C₂×#107	C₂²×C₅	1	1	yes	characteristic
212	C₂×#107	C₂²×C₅	1	1	yes	characteristic
213	C₂×#106	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
217	#396	—	2	1	no	—
218	#393	—	2	1	no	—
219	#391	—	2	1	no	—
220	#389	C₂²×C₅	1	1	yes	characteristic
221	#389	C₂²×C₅	1	1	yes	characteristic
222	#389	C₂²×C₅	1	1	yes	characteristic
223	#389	C₂²×C₅	1	1	yes	characteristic
224	#388	—	2	1	no	—
225	#388	—	2	1	no	—
226	#387	—	2	1	no	—
227	#382	—	2	1	no	—
228	#382	C₂²×C₅	1	1	yes	characteristic
229	#380	C₂²×C₅	1	1	yes	characteristic
230	#380	C₂²×C₅	1	1	yes	characteristic
231	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
232	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
233	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	#376	—	2	1	no	—
235	#340	C₂²×C₅	1	1	yes	characteristic
236	#340	C₂²×C₅	1	1	yes	characteristic
237	#340	C₂²×C₅	1	1	yes	characteristic
238	#340	C₂²×C₅	1	1	yes	characteristic
239	#340	C₂²×C₅	1	1	yes	characteristic
240	#340	C₂²×C₅	1	1	yes	characteristic
241	#340	C₂²×C₅	1	1	yes	characteristic
242	#340	C₂²×C₅	1	1	yes	characteristic
243	#340	C₂²×C₅	1	1	yes	characteristic
244	#340	C₂²×C₅	1	1	yes	characteristic
245	#340	C₂²×C₅	1	1	yes	characteristic
246	#340	C₂²×C₅	1	1	yes	characteristic
247	#336	C₂²×C₅	1	1	yes	characteristic
248	#336	C₂²×C₅	1	1	yes	characteristic
249	C₂³×C₅	—	2	1	no	—
250	C₂³×C₅	—	2	1	no	—
251	C₂³×C₅	—	2	1	no	—
252	C₂³×C₅	—	2	1	no	—
253	C₂³×C₅	—	2	1	no	—
254	C₂³×C₅	—	2	1	no	—
255	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
256	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₅×Q₈	—	8	4	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	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	—	4	1	no	—
279	C₂×C₄×C₅	—	4	1	no	—
280	C₂×C₄×C₅	—	4	1	no	—
281	C₂×C₄×C₅	—	4	1	no	—
282	C₂×C₄×C₅	—	4	1	no	—
283	C₂×C₄×C₅	—	4	1	no	—
284	C₂×C₄×C₅	—	4	1	no	—
285	C₂×C₄×C₅	—	4	1	no	—
286	C₂×C₄×C₅	—	4	1	no	—
287	C₂×C₄×C₅	—	4	1	no	—
288	C₂×C₄×C₅	—	4	1	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	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	C₂²⋊Q₈	1	2	yes	—
300	C₂×C₄×C₅	#135	1	2	yes	—
301	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
307	C₅×C₈	—	2	2	no	—
308	C₅×C₈	—	4	1	no	—
309	C₅×C₈	—	4	1	no	—
310	C₅×C₈	—	4	1	no	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	4	1	no	—
316	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	4	1	no	—
322	#117	—	2	2	no	—
323	#117	—	2	2	no	—
324	#117	—	4	1	no	—
325	#117	C₅×Q₈	1	4	yes	complemented
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
351	#107	—	2	2	no	—
352	#107	—	2	2	no	—
353	#107	—	4	1	no	—
354	#106	—	4	1	no	—
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	—	4	1	no	—
357	C₂²⋊C₈	—	2	2	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	#95	—	2	1	no	—
361	#95	—	2	1	no	—
362	#95	—	2	1	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	#95	C₅×D₄	1	1	yes	characteristic
369	#95	C₅×D₄	1	1	yes	characteristic
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	—	2	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	4	1	no	—
374	C₂²×C₅	—	4	1	no	—
375	C₂²×C₅	—	4	1	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
378	C₂²×C₅	#546	1	1	yes	characteristic
379	C₂²×C₅	#547	1	1	yes	characteristic
380	C₂²×C₅	C₂×#135	1	1	yes	characteristic
381	C₂²×C₅	#575	1	1	yes	characteristic
382	C₂²×C₅	#576	1	1	yes	characteristic
383	C₂²×C₅	#578	1	1	yes	characteristic
384	C₄×C₅	—	2	2	no	—
385	C₄×C₅	—	2	2	no	—
386	C₄×C₅	—	4	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	—	4	1	no	—
390	C₄×C₅	—	4	1	no	—
391	C₄×C₅	—	4	2	no	—
392	C₄×C₅	—	8	1	no	—
393	C₄×C₅	—	8	1	no	—
394	C₄×C₅	—	8	1	no	—
395	C₄×C₅	—	8	1	no	—
396	C₄×C₅	—	8	1	no	—
397	C₄×C₅	#533	1	1	yes	characteristic
398	C₄×C₅	#544	1	1	yes	characteristic
399	C₄×C₅	#551	1	1	yes	characteristic
400	C₄×C₅	#552	1	1	yes	characteristic
401	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂×Q₈	—	4	2	no	—
403	C₂×Q₈	—	4	2	no	—
404	C₂×Q₈	—	8	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
420	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
421	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
422	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
423	C₂²×C₄	C₅×#41	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	4	4	no	—
437	C₂×C₈	C₅×#41	1	2	yes	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	—	8	1	no	—
454	C₄⋊C₄	—	8	1	no	—
455	C₄⋊C₄	—	8	1	no	—
456	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
457	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
458	C₄⋊C₄	C₅×#41	1	2	yes	—
459	C₂²⋊C₄	—	2	4	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	4	1	no	—
462	C₂²⋊C₄	—	4	2	no	—
463	C₂²⋊C₄	—	8	1	no	—
464	C₂²⋊C₄	—	8	1	no	—
465	C₄²	—	2	4	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	4	2	no	—
471	C₄²	—	4	2	no	—
472	C₄²	—	4	2	no	—
473	C₂×C₅	—	4	2	no	—
474	C₂×C₅	#2438	1	1	yes	characteristic
475	C₂×C₅	#3076	1	1	yes	characteristic
476	C₂×C₅	#3083	1	1	yes	characteristic
477	C₂×C₅	#3300	1	1	yes	characteristic
478	C₂×C₅	#3319	1	1	yes	characteristic
479	C₂×C₅	#3341	1	1	yes	characteristic
480	C₂×C₅	#3349	1	1	yes	characteristic
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
488	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
489	Q₈	—	8	4	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
532	C₂×C₄	C₅×#135	1	2	yes	—
533	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
534	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
535	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
536	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
537	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
539	C₈	—	2	2	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₅	#25995	1	1	yes	characteristic, direct product factor, Sylow
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
552	C₂²	C₅×#546	1	1	yes	characteristic
553	C₂²	C₅×#547	1	1	yes	characteristic
554	C₂²	C₂×C₅×#135	1	1	yes	characteristic
555	C₂²	C₅×#575	1	1	yes	characteristic
556	C₂²	C₅×#576	1	1	yes	characteristic
557	C₂²	C₅×#578	1	1	yes	characteristic
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	8	1	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	1	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	C₅×#533	1	1	yes	characteristic
572	C₄	C₅×#544	1	1	yes	characteristic
573	C₄	C₅×#551	1	1	yes	characteristic
574	C₄	C₅×#552	1	1	yes	characteristic
575	C₂	—	4	2	no	—
576	C₂	C₅×#2438	1	1	yes	characteristic
577	C₂	C₅×#3076	1	1	yes	characteristic
578	C₂	C₅×#3083	1	1	yes	characteristic
579	C₂	C₅×#3300	1	1	yes	characteristic
580	C₂	C₅×#3319	1	1	yes	characteristic
581	C₂	C₅×#3341	1	1	yes	characteristic
582	C₂	C₅×#3349	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
3. C₅×#2101	C₂	semidirect
4. C₅×#2088	C₂	semidirect
5. C₅×#2086	C₂	semidirect
6. C₅×#2057	C₂	semidirect
7. C₅×#1987	C₂	semidirect
8. C₅×#1949	C₂	semidirect
9. C₅×#1921	C₂	semidirect
10. C₅×#1918	C₂	semidirect
59. #25995	C₅	direct (N × H)
74. C₅×#117	Q₈	semidirect
121. #2101	C₂×C₅	semidirect
122. #2088	C₂×C₅	semidirect
123. #2086	C₂×C₅	semidirect
124. #2057	C₂×C₅	semidirect
125. #1987	C₂×C₅	semidirect
126. #1949	C₂×C₅	semidirect
127. #1921	C₂×C₅	semidirect
128. #1918	C₂×C₅	semidirect
325. #117	C₅×Q₈	semidirect
543. C₅	#25995	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2439	2
C₅×#2346	2
C₅×#2101	2
C₅×#2088	2
C₅×#2086	2
C₅×#2057	2
C₅×#1987	2
C₅×#1949	2
C₅×#1921	2
C₅×#1918	2
C₅×#1854	2
C₅×#1850	2
C₅×#1825	2
C₅×#1808	2
C₅×#1735	2
#25995	5

Subgroups — C5×#25995 #11948715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25995 #11948715