Subgroups — C₅×#22587 #11945307

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2924	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic
3	C₅×#2880	C₂	1	1	yes	maximal, characteristic
4	C₅×#1937	C₂	1	2	yes	maximal, complemented
5	C₅×#1929	C₂	1	2	yes	maximal, complemented
6	C₅×#1866	C₂	1	2	yes	maximal, complemented
7	C₅×#1826	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1789	C₂	1	1	yes	maximal, characteristic
10	C₅×#1764	C₂	1	2	yes	maximal, complemented
11	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	C₂²	1	2	yes	—
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₅×#433	—	2	2	no	—
17	C₅×#432	—	2	1	no	—
18	C₅×#431	—	2	1	no	—
19	C₂×C₅×#108	C₂²	1	2	yes	complemented
20	C₅×#424	C₂²	1	2	yes	complemented
21	C₂×C₅×#104	C₂²	1	2	yes	—
22	C₂×C₅×#104	C₂²	1	2	yes	—
23	C₅×#416	C₄	1	1	yes	characteristic, complemented
24	C₅×#416	C₄	1	1	yes	characteristic, complemented
25	C₅×#416	C₄	1	1	yes	characteristic, complemented
26	C₅×#416	C₄	1	1	yes	characteristic, complemented
27	C₅×#416	C₂²	1	1	yes	characteristic
28	C₅×#416	C₂²	1	1	yes	characteristic
29	C₅×#416	C₂²	1	1	yes	characteristic
30	C₅×#416	C₂²	1	1	yes	characteristic
31	C₂×C₅×#103	C₄	1	1	yes	characteristic, complemented
32	C₂×C₅×#103	C₄	1	1	yes	characteristic, complemented
33	C₂×C₅×#102	C₄	1	1	yes	characteristic, complemented
34	C₂×C₅×#102	C₄	1	1	yes	characteristic, complemented
35	C₅×#408	—	2	2	no	—
36	C₅×#408	C₂²	1	2	yes	—
37	C₅×#407	—	2	1	no	—
38	C₅×#407	C₂²	1	1	yes	characteristic
39	C₅×#407	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
41	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₅×#405	C₂²	1	2	yes	complemented
43	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
44	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₅×#341	C₂²	1	2	yes	complemented
46	C₅×#339	C₂²	1	2	yes	complemented
47	C₅×#339	C₂²	1	2	yes	complemented
48	C₅×#336	C₂²	1	2	yes	complemented
49	#22587	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂×C₅×#41	—	2	1	no	—
52	C₂×C₅×#41	—	2	4	no	—
53	C₂×C₅×#41	—	4	2	no	—
54	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×#41	C₂³	1	1	yes	characteristic
57	C₂×C₅×#41	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₅×D₄	—	2	1	no	—
60	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₅	—	2	1	no	—
62	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₅×#131	—	2	4	no	—
64	C₅×#131	—	4	2	no	—
65	C₂×C₅×M₁₆	—	2	2	no	—
66	C₂×C₅×M₁₆	C₂³	1	2	yes	—
67	C₂×C₅×M₁₆	C₂³	1	2	yes	—
68	C₂²×C₅×C₈	—	2	2	no	—
69	C₂²×C₅×C₈	—	4	2	no	—
70	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	2	yes	—
77	C₅×#117	—	2	1	no	—
78	C₅×#117	—	2	1	no	—
79	C₅×#117	C₂×C₄	1	1	yes	characteristic
80	C₅×#117	C₂×C₄	1	1	yes	characteristic
81	C₅×#117	C₂³	1	1	yes	characteristic
82	C₅×#117	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	C₂³	1	2	yes	—
89	C₅×#108	—	4	2	no	—
90	C₅×C₄⋊C₈	—	2	2	no	—
91	C₅×C₄⋊C₈	—	2	2	no	—
92	C₅×#104	—	2	4	no	—
93	C₅×#104	—	4	2	no	—
94	C₅×#103	C₂×C₄	1	1	yes	characteristic
95	C₅×#103	C₂×C₄	1	1	yes	characteristic
96	C₅×#103	C₂×C₄	1	1	yes	characteristic
97	C₅×#103	C₂×C₄	1	1	yes	characteristic
98	C₅×#103	C₂×C₄	1	1	yes	characteristic
99	C₅×#103	C₂×C₄	1	1	yes	characteristic
100	C₅×#103	C₂×C₄	1	1	yes	characteristic
101	C₅×#103	C₂×C₄	1	1	yes	characteristic
102	C₅×#102	C₂×C₄	1	1	yes	characteristic
103	C₅×#102	C₂×C₄	1	1	yes	characteristic
104	C₅×#102	C₂×C₄	1	1	yes	characteristic
105	C₅×#102	C₂×C₄	1	1	yes	characteristic
106	C₅×#102	C₂×C₄	1	1	yes	characteristic
107	C₅×#102	C₂×C₄	1	1	yes	characteristic
108	C₅×#102	C₂×C₄	1	1	yes	characteristic
109	C₅×#102	C₂×C₄	1	1	yes	characteristic
110	C₅×C₂²⋊C₈	—	2	1	no	—
111	C₅×C₂²⋊C₈	—	2	1	no	—
112	C₅×C₂²⋊C₈	—	2	1	no	—
113	C₅×C₂²⋊C₈	—	2	1	no	—
114	C₅×C₂²⋊C₈	—	2	2	no	—
115	C₅×C₂²⋊C₈	—	2	2	no	—
116	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
117	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
118	C₅×C₂²⋊C₈	D₄	1	2	yes	—
119	C₅×#97	—	2	2	no	—
120	C₄×C₅×C₈	—	2	2	no	—
121	C₄×C₅×C₈	—	4	2	no	—
122	C₅×#95	—	2	1	no	—
123	#2924	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂×#416	C₂×C₅	1	1	yes	characteristic
125	#2880	C₂×C₅	1	1	yes	characteristic
126	#1937	C₂×C₅	1	2	yes	complemented
127	#1929	C₂×C₅	1	2	yes	complemented
128	#1866	C₂×C₅	1	2	yes	complemented
129	#1826	C₂×C₅	1	1	yes	characteristic, complemented
130	#1810	C₂×C₅	1	1	yes	characteristic, complemented
131	#1789	C₂×C₅	1	1	yes	characteristic
132	#1764	C₂×C₅	1	2	yes	complemented
133	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂⁴×C₅	—	2	1	no	—
135	C₂⁴×C₅	#41	1	1	yes	characteristic
136	C₅×#41	—	2	2	no	—
137	C₅×#41	—	2	2	no	—
138	C₅×#41	—	2	2	no	—
139	C₅×#41	—	2	2	no	—
140	C₅×#41	—	2	2	no	—
141	C₅×#41	—	4	4	no	—
142	C₅×#41	—	4	1	no	—
143	C₅×#41	—	4	1	no	—
144	C₅×#41	—	4	4	no	—
145	C₅×#41	#41	1	4	yes	—
146	C₂×C₅×Q₈	—	2	1	no	—
147	C₂×C₅×Q₈	—	2	2	no	—
148	C₂×C₅×Q₈	—	4	1	no	—
149	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	2	2	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	—	2	1	no	—
157	C₂×C₅×D₄	—	4	1	no	—
158	C₂×C₅×D₄	—	4	4	no	—
159	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	2	no	—
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	2	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	4	4	no	—
172	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	#41	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₅×M₁₆	—	2	2	no	—
179	C₅×M₁₆	—	2	2	no	—
180	C₅×M₁₆	—	2	2	no	—
181	C₅×M₁₆	—	2	2	no	—
182	C₅×M₁₆	—	4	4	no	—
183	C₂×C₅×C₈	—	2	2	no	—
184	C₂×C₅×C₈	—	2	2	no	—
185	C₂×C₅×C₈	—	2	2	no	—
186	C₂×C₅×C₈	—	2	2	no	—
187	C₂×C₅×C₈	—	2	2	no	—
188	C₂×C₅×C₈	—	2	2	no	—
189	C₂×C₅×C₈	—	4	1	no	—
190	C₂×C₅×C₈	—	4	1	no	—
191	C₂×C₅×C₈	—	4	1	no	—
192	C₂×C₅×C₈	—	4	1	no	—
193	C₂×C₅×C₈	—	4	4	no	—
194	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
199	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
203	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
206	C₅×C₂²⋊C₄	—	2	4	no	—
207	C₅×C₂²⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	—	2	1	no	—
209	C₅×C₂²⋊C₄	—	2	1	no	—
210	C₅×C₂²⋊C₄	—	2	1	no	—
211	C₄²×C₅	—	2	1	no	—
212	C₄²×C₅	—	2	1	no	—
213	C₄²×C₅	—	2	1	no	—
214	C₄²×C₅	—	2	1	no	—
215	C₄²×C₅	—	2	2	no	—
216	C₄²×C₅	—	2	2	no	—
217	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
218	C₂×#131	C₂²×C₅	1	2	yes	—
219	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
220	C₂×#117	C₂²×C₅	1	1	yes	characteristic
221	#433	—	2	2	no	—
222	#432	—	2	1	no	—
223	#431	—	2	1	no	—
224	C₂×#108	C₂²×C₅	1	2	yes	complemented
225	#424	C₂²×C₅	1	2	yes	complemented
226	C₂×#104	C₂²×C₅	1	2	yes	—
227	C₂×#104	C₂²×C₅	1	2	yes	—
228	#416	C₄×C₅	1	1	yes	characteristic, complemented
229	#416	C₄×C₅	1	1	yes	characteristic, complemented
230	#416	C₄×C₅	1	1	yes	characteristic, complemented
231	#416	C₄×C₅	1	1	yes	characteristic, complemented
232	#416	C₂²×C₅	1	1	yes	characteristic
233	#416	C₂²×C₅	1	1	yes	characteristic
234	#416	C₂²×C₅	1	1	yes	characteristic
235	#416	C₂²×C₅	1	1	yes	characteristic
236	C₂×#103	C₄×C₅	1	1	yes	characteristic, complemented
237	C₂×#103	C₄×C₅	1	1	yes	characteristic, complemented
238	C₂×#102	C₄×C₅	1	1	yes	characteristic, complemented
239	C₂×#102	C₄×C₅	1	1	yes	characteristic, complemented
240	#408	—	2	2	no	—
241	#408	C₂²×C₅	1	2	yes	—
242	#407	—	2	1	no	—
243	#407	C₂²×C₅	1	1	yes	characteristic
244	#407	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₂²⋊C₈	—	2	1	no	—
246	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
247	#405	C₂²×C₅	1	2	yes	complemented
248	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
249	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	#341	C₂²×C₅	1	2	yes	complemented
251	#339	C₂²×C₅	1	2	yes	complemented
252	#339	C₂²×C₅	1	2	yes	complemented
253	#336	C₂²×C₅	1	2	yes	complemented
254	C₂³×C₅	—	2	1	no	—
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	2	2	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	—	4	1	no	—
259	C₂³×C₅	—	4	2	no	—
260	C₂³×C₅	—	4	2	no	—
261	C₂³×C₅	—	8	1	no	—
262	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
263	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
264	C₂³×C₅	C₂×#41	1	1	yes	characteristic
265	C₅×Q₈	—	2	1	no	—
266	C₅×Q₈	—	2	1	no	—
267	C₅×Q₈	—	2	1	no	—
268	C₅×Q₈	—	4	2	no	—
269	C₅×Q₈	#117	1	2	yes	—
270	C₅×D₄	—	2	4	no	—
271	C₅×D₄	—	2	1	no	—
272	C₅×D₄	—	2	1	no	—
273	C₅×D₄	—	2	1	no	—
274	C₅×D₄	—	4	2	no	—
275	C₅×D₄	—	4	2	no	—
276	C₅×D₄	—	4	2	no	—
277	C₅×D₄	—	4	2	no	—
278	C₅×D₄	#117	1	2	yes	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	4	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	4	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	—	4	2	no	—
295	C₂×C₄×C₅	—	4	2	no	—
296	C₂×C₄×C₅	—	4	2	no	—
297	C₂×C₄×C₅	—	4	2	no	—
298	C₂×C₄×C₅	—	4	2	no	—
299	C₂×C₄×C₅	—	4	2	no	—
300	C₂×C₄×C₅	—	4	2	no	—
301	C₂×C₄×C₅	—	8	1	no	—
302	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×#41	1	2	yes	—
307	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
308	C₅×C₈	—	2	1	no	—
309	C₅×C₈	—	2	1	no	—
310	C₅×C₈	—	2	1	no	—
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	2	no	—
313	C₅×C₈	—	2	2	no	—
314	C₅×C₈	—	4	2	no	—
315	C₅×C₈	—	4	2	no	—
316	C₂×#41	—	2	1	no	—
317	C₂×#41	—	2	1	no	—
318	C₂×#41	—	2	4	no	—
319	C₂×#41	—	4	2	no	—
320	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
321	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
322	C₂×#41	C₂³×C₅	1	1	yes	characteristic
323	C₂×#41	C₂³×C₅	1	1	yes	characteristic
324	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
329	#131	—	2	4	no	—
330	#131	—	4	2	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	C₂³×C₅	1	2	yes	—
333	C₂×M₁₆	C₂³×C₅	1	2	yes	—
334	C₂²×C₈	—	2	2	no	—
335	C₂²×C₈	—	4	2	no	—
336	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
337	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
338	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
339	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₅	1	2	yes	—
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	C₂×C₄×C₅	1	1	yes	characteristic
346	#117	C₂×C₄×C₅	1	1	yes	characteristic
347	#117	C₂³×C₅	1	1	yes	characteristic
348	#117	C₂³×C₅	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	C₂³×C₅	1	2	yes	—
355	#108	—	4	2	no	—
356	C₄⋊C₈	—	2	2	no	—
357	C₄⋊C₈	—	2	2	no	—
358	#104	—	2	4	no	—
359	#104	—	4	2	no	—
360	#103	C₂×C₄×C₅	1	1	yes	characteristic
361	#103	C₂×C₄×C₅	1	1	yes	characteristic
362	#103	C₂×C₄×C₅	1	1	yes	characteristic
363	#103	C₂×C₄×C₅	1	1	yes	characteristic
364	#103	C₂×C₄×C₅	1	1	yes	characteristic
365	#103	C₂×C₄×C₅	1	1	yes	characteristic
366	#103	C₂×C₄×C₅	1	1	yes	characteristic
367	#103	C₂×C₄×C₅	1	1	yes	characteristic
368	#102	C₂×C₄×C₅	1	1	yes	characteristic
369	#102	C₂×C₄×C₅	1	1	yes	characteristic
370	#102	C₂×C₄×C₅	1	1	yes	characteristic
371	#102	C₂×C₄×C₅	1	1	yes	characteristic
372	#102	C₂×C₄×C₅	1	1	yes	characteristic
373	#102	C₂×C₄×C₅	1	1	yes	characteristic
374	#102	C₂×C₄×C₅	1	1	yes	characteristic
375	#102	C₂×C₄×C₅	1	1	yes	characteristic
376	C₂²⋊C₈	—	2	1	no	—
377	C₂²⋊C₈	—	2	1	no	—
378	C₂²⋊C₈	—	2	1	no	—
379	C₂²⋊C₈	—	2	1	no	—
380	C₂²⋊C₈	—	2	2	no	—
381	C₂²⋊C₈	—	2	2	no	—
382	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
383	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
384	C₂²⋊C₈	C₅×D₄	1	2	yes	—
385	#97	—	2	2	no	—
386	C₄×C₈	—	2	2	no	—
387	C₄×C₈	—	4	2	no	—
388	#95	—	2	1	no	—
389	C₂²×C₅	—	2	1	no	—
390	C₂²×C₅	—	2	1	no	—
391	C₂²×C₅	—	2	1	no	—
392	C₂²×C₅	—	2	1	no	—
393	C₂²×C₅	—	2	1	no	—
394	C₂²×C₅	—	2	2	no	—
395	C₂²×C₅	—	2	1	no	—
396	C₂²×C₅	—	2	1	no	—
397	C₂²×C₅	—	4	4	no	—
398	C₂²×C₅	—	4	1	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	—	4	1	no	—
403	C₂²×C₅	—	8	4	no	—
404	C₂²×C₅	#443	1	2	yes	—
405	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
406	C₂²×C₅	#551	1	2	yes	—
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	4	4	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	1	no	—
413	C₄×C₅	—	4	1	no	—
414	C₄×C₅	—	4	1	no	—
415	C₄×C₅	—	4	1	no	—
416	C₄×C₅	C₂×#117	1	1	yes	characteristic
417	C₄×C₅	#518	1	1	yes	characteristic
418	C₄×C₅	#546	1	2	yes	—
419	C₂⁴	—	2	1	no	—
420	C₂⁴	C₅×#41	1	1	yes	characteristic
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	4	4	no	—
427	#41	—	4	1	no	—
428	#41	—	4	1	no	—
429	#41	—	4	4	no	—
430	#41	C₅×#41	1	4	yes	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	4	1	no	—
434	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
435	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	4	no	—
444	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
445	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
458	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
461	C₂²×C₄	C₅×#41	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	4	4	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	4	1	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	4	no	—
479	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
480	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
481	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
482	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
483	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
484	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₂×C₅	—	2	2	no	—
503	C₂×C₅	—	2	2	no	—
504	C₂×C₅	—	4	1	no	—
505	C₂×C₅	—	4	2	no	—
506	C₂×C₅	—	8	1	no	—
507	C₂×C₅	#2342	1	1	yes	characteristic
508	C₂×C₅	C₂×#443	1	1	yes	characteristic
509	C₂×C₅	#2957	1	1	yes	characteristic
510	C₂³	—	2	2	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	8	1	no	—
518	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
519	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
520	C₂³	C₂×C₅×#41	1	1	yes	characteristic
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	4	2	no	—
525	Q₈	C₅×#117	1	2	yes	—
526	D₄	—	2	4	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	C₅×#117	1	2	yes	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	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	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	8	1	no	—
558	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
559	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
560	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
561	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
562	C₂×C₄	C₂×C₅×#41	1	2	yes	—
563	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₈	—	4	2	no	—
571	C₈	—	4	2	no	—
572	C₅	#22587	1	1	yes	characteristic, direct product factor, Sylow
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	8	4	no	—
588	C₂²	C₅×#443	1	2	yes	—
589	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
590	C₂²	C₅×#551	1	2	yes	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	C₂×C₅×#117	1	1	yes	characteristic
601	C₄	C₅×#518	1	1	yes	characteristic
602	C₄	C₅×#546	1	2	yes	—
603	C₂	—	2	2	no	—
604	C₂	—	2	2	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	8	1	no	—
608	C₂	C₅×#2342	1	1	yes	characteristic
609	C₂	C₂×C₅×#443	1	1	yes	characteristic
610	C₂	C₅×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2924	C₂	semidirect
4. C₅×#1937	C₂	semidirect
5. C₅×#1929	C₂	semidirect
6. C₅×#1866	C₂	semidirect
7. C₅×#1826	C₂	semidirect
8. C₅×#1810	C₂	semidirect
10. C₅×#1764	C₂	semidirect
11. C₅×C₈×C₂²⋊C₄	C₂	semidirect
19. C₂×C₅×#108	C₂²	semidirect
20. C₅×#424	C₂²	semidirect
23. C₅×#416	C₄	semidirect
24. C₅×#416	C₄	semidirect
25. C₅×#416	C₄	semidirect
26. C₅×#416	C₄	semidirect
31. C₂×C₅×#103	C₄	semidirect
32. C₂×C₅×#103	C₄	semidirect
33. C₂×C₅×#102	C₄	semidirect
34. C₂×C₅×#102	C₄	semidirect
42. C₅×#405	C₂²	semidirect
43. C₂×C₄×C₅×C₈	C₂²	semidirect
45. C₅×#341	C₂²	semidirect
46. C₅×#339	C₂²	semidirect
47. C₅×#339	C₂²	semidirect
48. C₅×#336	C₂²	semidirect
49. #22587	C₅	direct (N × H)
123. #2924	C₂×C₅	semidirect
126. #1937	C₂×C₅	semidirect
127. #1929	C₂×C₅	semidirect
128. #1866	C₂×C₅	semidirect
129. #1826	C₂×C₅	semidirect
130. #1810	C₂×C₅	semidirect
132. #1764	C₂×C₅	semidirect
133. C₈×C₂²⋊C₄	C₂×C₅	semidirect
224. C₂×#108	C₂²×C₅	semidirect
225. #424	C₂²×C₅	semidirect
228. #416	C₄×C₅	semidirect
229. #416	C₄×C₅	semidirect
230. #416	C₄×C₅	semidirect
231. #416	C₄×C₅	semidirect
236. C₂×#103	C₄×C₅	semidirect
237. C₂×#103	C₄×C₅	semidirect
238. C₂×#102	C₄×C₅	semidirect
239. C₂×#102	C₄×C₅	semidirect
247. #405	C₂²×C₅	semidirect
248. C₂×C₄×C₈	C₂²×C₅	semidirect
250. #341	C₂²×C₅	semidirect
251. #339	C₂²×C₅	semidirect
252. #339	C₂²×C₅	semidirect
253. #336	C₂²×C₅	semidirect
572. C₅	#22587	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×#2924	2
C₂×C₅×#416	2
C₅×#2880	2
C₅×#1937	2
C₅×#1929	2
C₅×#1866	2
C₅×#1826	2
C₅×#1810	2
C₅×#1789	2
C₅×#1764	2
C₅×C₈×C₂²⋊C₄	2
#22587	5

Subgroups — C5×#22587 #11945307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22587 #11945307