Subgroups — C₅×#23093 #11945813

Order 1280.

1042 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#459	C₂	1	1	yes	maximal, characteristic
2	C₅×#2366	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1970	C₂	1	2	yes	maximal, complemented
5	C₅×#1957	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1925	C₂	1	2	yes	maximal, complemented
8	C₅×#1879	C₂	1	2	yes	maximal, complemented
9	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#102	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×D₈	C₂²	1	2	yes	—
13	C₂×C₅×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	—	2	1	no	—
15	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₅×#117	—	2	1	no	—
18	C₅×#459	C₄	1	8	yes	complemented
19	C₂×C₅×#107	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#102	C₂²	1	1	yes	characteristic
22	C₂×C₅×#102	C₂²	1	2	yes	—
23	C₂×C₅×#102	C₂²	1	1	yes	characteristic
24	C₂×C₅×#102	C₂²	1	2	yes	—
25	C₂×C₅×#102	C₂²	1	2	yes	—
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
28	C₅×#390	—	2	1	no	—
29	C₅×#390	C₂²	1	2	yes	—
30	C₅×#390	C₂²	1	2	yes	—
31	C₅×#388	—	2	2	no	—
32	C₅×#386	—	2	2	no	—
33	C₅×#384	C₂²	1	1	yes	characteristic
34	C₅×#380	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	2	yes	—
42	#23093	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×D₄	—	2	1	no	—
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
46	C₂²×C₅×D₄	C₂³	1	2	yes	—
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂³×C₄×C₅	—	2	2	no	—
49	C₂×C₅×D₈	—	4	2	no	—
50	C₂×C₅×D₈	—	4	2	no	—
51	C₂×C₅×D₈	C₂×C₄	1	8	yes	complemented
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₅×#127	—	2	2	no	—
56	C₅×#127	C₂×C₄	1	4	yes	—
57	C₄×C₅×D₄	—	2	4	no	—
58	C₄×C₅×D₄	—	2	2	no	—
59	C₄×C₅×D₄	—	4	2	no	—
60	C₄×C₅×D₄	—	4	4	no	—
61	C₄×C₅×D₄	C₂×C₄	1	4	yes	complemented
62	C₅×#117	—	4	4	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₄²×C₅	—	2	2	no	—
78	C₂×C₄²×C₅	—	2	1	no	—
79	C₂×C₄²×C₅	C₂³	1	2	yes	—
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₅×#107	—	4	2	no	—
82	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
83	C₅×#102	—	2	4	no	—
84	C₅×#102	—	2	2	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#102	—	4	2	no	—
87	C₅×#102	C₂×C₄	1	8	yes	complemented
88	C₄×C₅×C₈	—	2	2	no	—
89	C₄×C₅×C₈	—	4	2	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	—	2	1	no	—
92	C₅×#95	D₄	1	2	yes	—
93	C₂×#459	C₂×C₅	1	1	yes	characteristic
94	#2366	C₂×C₅	1	1	yes	characteristic, complemented
95	#2354	C₂×C₅	1	1	yes	characteristic, complemented
96	#1970	C₂×C₅	1	2	yes	complemented
97	#1957	C₂×C₅	1	1	yes	characteristic, complemented
98	#1947	C₂×C₅	1	1	yes	characteristic, complemented
99	#1925	C₂×C₅	1	2	yes	complemented
100	#1879	C₂×C₅	1	2	yes	complemented
101	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
102	C₄×#102	C₂×C₅	1	2	yes	complemented
103	C₄×#102	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	—	2	1	no	—
105	C₂⁴×C₅	—	2	2	no	—
106	C₂×C₅×D₄	—	2	4	no	—
107	C₂×C₅×D₄	—	2	4	no	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	2	1	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	1	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	4	2	no	—
119	C₂×C₅×D₄	—	4	2	no	—
120	C₂×C₅×D₄	—	8	1	no	—
121	C₂×C₅×D₄	—	8	1	no	—
122	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
123	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	4	4	no	—
130	C₂²×C₄×C₅	—	4	2	no	—
131	C₂²×C₄×C₅	—	4	2	no	—
132	C₂²×C₄×C₅	—	4	4	no	—
133	C₂²×C₄×C₅	—	8	2	no	—
134	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₅×D₈	—	4	8	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
148	C₂×C₅×C₈	#41	1	2	yes	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	4	2	no	—
157	C₅×C₄⋊C₄	—	8	1	no	—
158	C₅×C₄⋊C₄	D₈	1	4	yes	complemented
159	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
160	C₅×C₄⋊C₄	#41	1	2	yes	—
161	C₅×C₂²⋊C₄	—	2	4	no	—
162	C₅×C₂²⋊C₄	—	4	4	no	—
163	C₅×C₂²⋊C₄	—	4	4	no	—
164	C₅×C₂²⋊C₄	—	4	4	no	—
165	C₅×C₂²⋊C₄	—	8	2	no	—
166	C₅×C₂²⋊C₄	—	8	2	no	—
167	C₄²×C₅	—	2	2	no	—
168	C₄²×C₅	—	2	2	no	—
169	C₄²×C₅	—	4	4	no	—
170	C₄²×C₅	—	4	2	no	—
171	C₄²×C₅	C₂²×C₄	1	2	yes	—
172	C₄²×C₅	#41	1	2	yes	—
173	C₂²×D₈	C₂²×C₅	1	2	yes	—
174	C₂×#127	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₄×D₄	—	2	1	no	—
176	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
177	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×#117	—	2	1	no	—
179	#459	C₄×C₅	1	8	yes	complemented
180	C₂×#107	C₂²×C₅	1	2	yes	—
181	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
182	C₂×#102	C₂²×C₅	1	1	yes	characteristic
183	C₂×#102	C₂²×C₅	1	2	yes	—
184	C₂×#102	C₂²×C₅	1	1	yes	characteristic
185	C₂×#102	C₂²×C₅	1	2	yes	—
186	C₂×#102	C₂²×C₅	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
189	#390	—	2	1	no	—
190	#390	C₂²×C₅	1	2	yes	—
191	#390	C₂²×C₅	1	2	yes	—
192	#388	—	2	2	no	—
193	#386	—	2	2	no	—
194	#384	C₂²×C₅	1	1	yes	characteristic
195	#380	—	2	1	no	—
196	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
197	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	#340	C₂²×C₅	1	2	yes	—
200	#340	C₂²×C₅	1	1	yes	characteristic
201	#340	C₂²×C₅	1	1	yes	characteristic
202	#336	C₂²×C₅	1	2	yes	—
203	C₂³×C₅	—	2	2	no	—
204	C₂³×C₅	—	2	4	no	—
205	C₂³×C₅	—	4	2	no	—
206	C₂³×C₅	—	4	1	no	—
207	C₂³×C₅	—	4	1	no	—
208	C₂³×C₅	—	4	2	no	—
209	C₂³×C₅	—	4	1	no	—
210	C₂³×C₅	—	4	2	no	—
211	C₂³×C₅	—	4	1	no	—
212	C₂³×C₅	—	4	2	no	—
213	C₂³×C₅	—	4	1	no	—
214	C₂³×C₅	—	4	2	no	—
215	C₂³×C₅	—	4	2	no	—
216	C₂³×C₅	—	4	1	no	—
217	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₅×D₄	—	2	4	no	—
219	C₅×D₄	—	2	2	no	—
220	C₅×D₄	—	2	2	no	—
221	C₅×D₄	—	2	4	no	—
222	C₅×D₄	—	4	1	no	—
223	C₅×D₄	—	4	2	no	—
224	C₅×D₄	—	4	2	no	—
225	C₅×D₄	—	4	1	no	—
226	C₅×D₄	—	4	8	no	—
227	C₅×D₄	—	8	4	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	8	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	8	8	no	—
249	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
251	C₂×C₄×C₅	C₂×D₈	1	4	yes	—
252	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
253	C₂×C₄×C₅	#135	1	2	yes	—
254	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
260	C₅×C₈	—	2	4	no	—
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	4	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	C₂³×C₅	1	2	yes	—
266	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	—	2	2	no	—
269	C₂×D₈	—	4	2	no	—
270	C₂×D₈	—	4	2	no	—
271	C₂×D₈	C₂×C₄×C₅	1	8	yes	complemented
272	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₅	1	2	yes	—
274	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
275	#127	—	2	2	no	—
276	#127	C₂×C₄×C₅	1	4	yes	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	4	2	no	—
280	C₄×D₄	—	4	4	no	—
281	C₄×D₄	C₂×C₄×C₅	1	4	yes	complemented
282	#117	—	4	4	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₅	1	2	yes	—
300	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
301	#107	—	4	2	no	—
302	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
303	#102	—	2	4	no	—
304	#102	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	4	2	no	—
307	#102	C₂×C₄×C₅	1	8	yes	complemented
308	C₄×C₈	—	2	2	no	—
309	C₄×C₈	—	4	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	1	no	—
312	#95	C₅×D₄	1	2	yes	—
313	C₂²×C₅	—	4	2	no	—
314	C₂²×C₅	—	4	4	no	—
315	C₂²×C₅	—	4	2	no	—
316	C₂²×C₅	—	4	4	no	—
317	C₂²×C₅	—	4	4	no	—
318	C₂²×C₅	—	4	2	no	—
319	C₂²×C₅	—	8	1	no	—
320	C₂²×C₅	—	8	2	no	—
321	C₂²×C₅	—	8	1	no	—
322	C₂²×C₅	—	8	2	no	—
323	C₂²×C₅	—	8	2	no	—
324	C₂²×C₅	—	8	1	no	—
325	C₂²×C₅	—	8	2	no	—
326	C₂²×C₅	—	8	1	no	—
327	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
328	C₂²×C₅	#546	1	1	yes	characteristic
329	C₂²×C₅	#550	1	1	yes	characteristic
330	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
331	C₂²×C₅	C₂×#135	1	1	yes	characteristic
332	C₂²×C₅	#576	1	1	yes	characteristic
333	C₂²×C₅	#577	1	1	yes	characteristic
334	C₄×C₅	—	2	2	no	—
335	C₄×C₅	—	2	4	no	—
336	C₄×C₅	—	4	2	no	—
337	C₄×C₅	—	4	2	no	—
338	C₄×C₅	—	4	2	no	—
339	C₄×C₅	—	8	1	no	—
340	C₄×C₅	—	8	2	no	—
341	C₄×C₅	C₄×D₈	1	4	yes	—
342	C₄×C₅	C₄×#41	1	1	yes	characteristic
343	C₄×C₅	#518	1	1	yes	characteristic
344	C₄×C₅	#553	1	1	yes	characteristic
345	C₄×C₅	#555	1	1	yes	characteristic
346	C₂⁴	—	2	1	no	—
347	C₂⁴	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	8	1	no	—
363	C₂×D₄	—	8	1	no	—
364	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
365	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	8	2	no	—
376	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
377	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
379	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
381	D₈	—	4	8	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
390	C₂×C₈	C₅×#41	1	2	yes	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	8	1	no	—
400	C₄⋊C₄	C₅×D₈	1	4	yes	complemented
401	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
402	C₄⋊C₄	C₅×#41	1	2	yes	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	4	4	no	—
405	C₂²⋊C₄	—	4	4	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	8	2	no	—
408	C₂²⋊C₄	—	8	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	4	4	no	—
412	C₄²	—	4	2	no	—
413	C₄²	C₂²×C₄×C₅	1	2	yes	—
414	C₄²	C₅×#41	1	2	yes	—
415	C₂×C₅	—	8	2	no	—
416	C₂×C₅	—	8	4	no	—
417	C₂×C₅	#2363	1	1	yes	characteristic
418	C₂×C₅	C₂×C₄×D₈	1	1	yes	characteristic
419	C₂×C₅	#2946	1	1	yes	characteristic
420	C₂×C₅	#3294	1	1	yes	characteristic
421	C₂×C₅	#3305	1	1	yes	characteristic
422	C₂×C₅	#3391	1	1	yes	characteristic
423	C₂×C₅	#3394	1	1	yes	characteristic
424	C₂³	—	2	2	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	1	no	—
438	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
439	D₄	—	2	2	no	—
440	D₄	—	2	4	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	4	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	1	no	—
447	D₄	—	4	2	no	—
448	D₄	—	8	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	8	8	no	—
470	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
471	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
472	C₂×C₄	C₂×C₅×D₈	1	4	yes	—
473	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
474	C₂×C₄	C₅×#135	1	2	yes	—
475	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
476	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
477	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
478	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
479	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
481	C₈	—	2	4	no	—
482	C₈	—	2	2	no	—
483	C₈	—	4	1	no	—
484	C₅	#23093	1	1	yes	characteristic, direct product factor, Sylow
485	C₂²	—	4	2	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	1	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	2	no	—
499	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
500	C₂²	C₅×#546	1	1	yes	characteristic
501	C₂²	C₅×#550	1	1	yes	characteristic
502	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
503	C₂²	C₂×C₅×#135	1	1	yes	characteristic
504	C₂²	C₅×#576	1	1	yes	characteristic
505	C₂²	C₅×#577	1	1	yes	characteristic
506	C₄	—	2	4	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	8	1	no	—
512	C₄	—	8	2	no	—
513	C₄	C₄×C₅×D₈	1	4	yes	—
514	C₄	C₄×C₅×#41	1	1	yes	characteristic
515	C₄	C₅×#518	1	1	yes	characteristic
516	C₄	C₅×#553	1	1	yes	characteristic
517	C₄	C₅×#555	1	1	yes	characteristic
518	C₂	—	8	2	no	—
519	C₂	—	8	4	no	—
520	C₂	C₅×#2363	1	1	yes	characteristic
521	C₂	C₂×C₄×C₅×D₈	1	1	yes	characteristic
522	C₂	C₅×#2946	1	1	yes	characteristic
523	C₂	C₅×#3294	1	1	yes	characteristic
524	C₂	C₅×#3305	1	1	yes	characteristic
525	C₂	C₅×#3391	1	1	yes	characteristic
526	C₂	C₅×#3394	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	C₂×C₅×#459	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2366	C₂	semidirect
3. C₅×#2354	C₂	semidirect
4. C₅×#1970	C₂	semidirect
5. C₅×#1957	C₂	semidirect
6. C₅×#1947	C₂	semidirect
7. C₅×#1925	C₂	semidirect
8. C₅×#1879	C₂	semidirect
9. C₅×C₈×C₄⋊C₄	C₂	semidirect
10. C₄×C₅×#102	C₂	semidirect
11. C₄×C₅×#102	C₂	semidirect
18. C₅×#459	C₄	semidirect
42. #23093	C₅	direct (N × H)
51. C₂×C₅×D₈	C₂×C₄	semidirect
61. C₄×C₅×D₄	C₂×C₄	semidirect
82. C₅×C₄⋊C₈	C₂×C₄	semidirect
87. C₅×#102	C₂×C₄	semidirect
94. #2366	C₂×C₅	semidirect
95. #2354	C₂×C₅	semidirect
96. #1970	C₂×C₅	semidirect
97. #1957	C₂×C₅	semidirect
98. #1947	C₂×C₅	semidirect
99. #1925	C₂×C₅	semidirect
100. #1879	C₂×C₅	semidirect
101. C₈×C₄⋊C₄	C₂×C₅	semidirect
102. C₄×#102	C₂×C₅	semidirect
103. C₄×#102	C₂×C₅	semidirect
158. C₅×C₄⋊C₄	D₈	semidirect
179. #459	C₄×C₅	semidirect
271. C₂×D₈	C₂×C₄×C₅	semidirect
281. C₄×D₄	C₂×C₄×C₅	semidirect
302. C₄⋊C₈	C₂×C₄×C₅	semidirect
307. #102	C₂×C₄×C₅	semidirect
400. C₄⋊C₄	C₅×D₈	semidirect
484. C₅	#23093	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×#459	2
C₅×#2366	2
C₅×#2354	2
C₅×#1970	2
C₅×#1957	2
C₅×#1947	2
C₅×#1925	2
C₅×#1879	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#102	2
#23093	5

Subgroups — C5×#23093 #11945813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23093 #11945813