Subgroups — C₅×#23030 #11945750

Order 1280.

926 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
4	C₅×#2362	C₂	1	2	yes	maximal
5	C₅×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1928	C₂	1	2	yes	maximal, complemented
8	C₅×#1873	C₂	1	2	yes	maximal
9	C₅×#1863	C₂	1	2	yes	maximal, complemented
10	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1752	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₂×C₅×#117	C₂²	1	2	yes	—
17	C₅×#467	C₄	1	8	yes	complemented
18	C₅×#441	—	2	4	no	—
19	C₅×#427	—	2	4	no	—
20	C₂×C₅×#107	C₂²	1	2	yes	—
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×#106	C₂²	1	1	yes	characteristic
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#103	C₂²	1	2	yes	—
27	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₅×#391	C₂²	1	2	yes	—
31	C₅×#389	C₂²	1	2	yes	—
32	C₅×#388	—	2	2	no	—
33	C₅×#388	—	2	2	no	—
34	C₅×#387	—	2	2	no	—
35	C₄×C₅×C₄⋊C₄	—	2	2	no	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	1	yes	characteristic
42	#23030	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₅×Q₁₆	—	2	2	no	—
46	C₂×C₅×Q₁₆	—	2	2	no	—
47	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	—
48	C₂²×C₅×C₈	—	2	2	no	—
49	C₂²×C₅×C₈	—	2	2	no	—
50	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₅×C₂²⋊Q₈	—	2	4	no	—
56	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
57	C₄×C₅×Q₈	—	2	4	no	—
58	C₄×C₅×Q₈	—	4	2	no	—
59	C₅×#117	—	2	4	no	—
60	C₅×#117	—	4	2	no	—
61	C₂×C₅×C₄⋊C₄	—	2	2	no	—
62	C₂×C₅×C₄⋊C₄	—	2	2	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
70	C₂×C₄²×C₅	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	—	2	2	no	—
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	—	2	4	no	—
76	C₅×#107	C₂×C₄	1	4	yes	—
77	C₅×#106	—	2	2	no	—
78	C₅×#106	D₄	1	4	yes	—
79	C₅×#103	—	2	4	no	—
80	C₅×#103	—	4	2	no	—
81	C₅×#103	C₂×C₄	1	8	yes	—
82	C₅×C₂²⋊C₈	—	2	2	no	—
83	C₅×#97	—	2	2	no	—
84	C₅×#97	—	2	2	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	—	2	2	no	—
87	C₅×#95	—	2	2	no	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	D₄	1	2	yes	—
90	C₂×#467	C₂×C₅	1	1	yes	characteristic
91	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#427	C₂×C₅	1	1	yes	characteristic
93	#2362	C₂×C₅	1	2	yes	—
94	#1971	C₂×C₅	1	1	yes	characteristic, complemented
95	#1943	C₂×C₅	1	1	yes	characteristic, complemented
96	#1928	C₂×C₅	1	2	yes	complemented
97	#1873	C₂×C₅	1	2	yes	—
98	#1863	C₂×C₅	1	2	yes	complemented
99	#1776	C₂×C₅	1	1	yes	characteristic, complemented
100	#1752	C₂×C₅	1	1	yes	characteristic
101	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₅×Q₈	—	2	2	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	#41	1	2	yes	—
121	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₅×Q₁₆	—	2	8	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	8	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
135	C₂×C₅×C₈	#41	1	2	yes	—
136	C₅×C₄⋊C₄	—	2	8	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	4	4	no	—
142	C₅×C₄⋊C₄	—	4	4	no	—
143	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
144	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
145	C₅×C₂²⋊C₄	—	2	8	no	—
146	C₅×C₂²⋊C₄	—	4	2	no	—
147	C₅×C₂²⋊C₄	—	4	4	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	—	2	1	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄²×C₅	—	2	1	no	—
152	C₄²×C₅	—	4	4	no	—
153	C₄²×C₅	—	4	4	no	—
154	C₄²×C₅	—	4	4	no	—
155	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
156	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
158	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
159	C₂×#117	C₂²×C₅	1	2	yes	—
160	#467	C₄×C₅	1	8	yes	complemented
161	#441	—	2	4	no	—
162	#427	—	2	4	no	—
163	C₂×#107	C₂²×C₅	1	2	yes	—
164	C₂×#107	C₂²×C₅	1	1	yes	characteristic
165	C₂×#106	C₂²×C₅	1	1	yes	characteristic
166	C₂×#106	C₂²×C₅	1	1	yes	characteristic
167	C₂×#103	C₂²×C₅	1	2	yes	—
168	C₂×#103	C₂²×C₅	1	2	yes	—
169	C₂×#103	C₂²×C₅	1	2	yes	—
170	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
171	C₂×#97	C₂²×C₅	1	1	yes	characteristic
172	C₂×#97	C₂²×C₅	1	1	yes	characteristic
173	#391	C₂²×C₅	1	2	yes	—
174	#389	C₂²×C₅	1	2	yes	—
175	#388	—	2	2	no	—
176	#388	—	2	2	no	—
177	#387	—	2	2	no	—
178	C₄×C₄⋊C₄	—	2	2	no	—
179	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
180	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
181	#340	C₂²×C₅	1	2	yes	—
182	#340	C₂²×C₅	1	2	yes	—
183	#336	C₂²×C₅	1	1	yes	characteristic
184	#336	C₂²×C₅	1	1	yes	characteristic
185	C₂³×C₅	—	2	1	no	—
186	C₂³×C₅	—	2	1	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	—	2	2	no	—
189	C₂³×C₅	C₄×D₄	1	2	yes	—
190	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
191	C₅×Q₈	—	2	4	no	—
192	C₅×Q₈	—	2	4	no	—
193	C₅×Q₈	—	4	2	no	—
194	C₅×Q₈	—	4	2	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
226	C₅×C₈	—	2	2	no	—
227	C₅×C₈	—	4	1	no	—
228	C₅×C₈	—	4	1	no	—
229	C₅×C₈	C₄×D₄	1	4	yes	—
230	C₂²×Q₈	C₂³×C₅	1	2	yes	—
231	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
232	C₂×Q₁₆	—	2	2	no	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
238	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
242	C₂²⋊Q₈	—	2	4	no	—
243	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	—
244	C₄×Q₈	—	2	4	no	—
245	C₄×Q₈	—	4	2	no	—
246	#117	—	2	4	no	—
247	#117	—	4	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
262	#107	—	2	4	no	—
263	#107	C₂×C₄×C₅	1	4	yes	—
264	#106	—	2	2	no	—
265	#106	C₅×D₄	1	4	yes	—
266	#103	—	2	4	no	—
267	#103	—	4	2	no	—
268	#103	C₂×C₄×C₅	1	8	yes	—
269	C₂²⋊C₈	—	2	2	no	—
270	#97	—	2	2	no	—
271	#97	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	C₅×D₄	1	2	yes	—
277	C₂²×C₅	—	2	2	no	—
278	C₂²×C₅	—	2	2	no	—
279	C₂²×C₅	—	2	2	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂²×C₅	D₄²	1	1	yes	characteristic
284	C₂²×C₅	#547	1	1	yes	characteristic
285	C₂²×C₅	#575	1	2	yes	—
286	C₂²×C₅	#578	1	2	yes	—
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	4	4	no	—
290	C₄×C₅	—	4	4	no	—
291	C₄×C₅	—	4	2	no	—
292	C₄×C₅	—	4	4	no	—
293	C₄×C₅	—	8	2	no	—
294	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
295	C₄×C₅	#520	1	1	yes	characteristic
296	C₄×C₅	#548	1	1	yes	characteristic
297	C₄×C₅	#553	1	1	yes	characteristic
298	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
314	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
315	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
316	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₅×#41	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
319	Q₁₆	—	2	8	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	8	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
330	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
331	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
332	C₂×C₈	C₅×#41	1	2	yes	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
341	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	4	4	no	—
350	C₄²	—	4	4	no	—
351	C₄²	—	4	4	no	—
352	C₂×C₅	—	4	2	no	—
353	C₂×C₅	#2361	1	1	yes	characteristic
354	C₂×C₅	#2943	1	1	yes	characteristic
355	C₂×C₅	#2950	1	1	yes	characteristic
356	C₂×C₅	#3269	1	2	yes	—
357	C₂×C₅	#3349	1	2	yes	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	C₄×C₅×D₄	1	2	yes	—
363	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
364	Q₈	—	2	4	no	—
365	Q₈	—	2	4	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
393	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
395	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
396	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
397	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
399	C₈	—	2	2	no	—
400	C₈	—	4	1	no	—
401	C₈	—	4	1	no	—
402	C₈	C₄×C₅×D₄	1	4	yes	—
403	C₅	#23030	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
410	C₂²	C₅×D₄²	1	1	yes	characteristic
411	C₂²	C₅×#547	1	1	yes	characteristic
412	C₂²	C₅×#575	1	2	yes	—
413	C₂²	C₅×#578	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	4	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	4	no	—
420	C₄	—	8	2	no	—
421	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
422	C₄	C₅×#520	1	1	yes	characteristic
423	C₄	C₅×#548	1	1	yes	characteristic
424	C₄	C₅×#553	1	1	yes	characteristic
425	C₂	—	4	2	no	—
426	C₂	C₅×#2361	1	1	yes	characteristic
427	C₂	C₅×#2943	1	1	yes	characteristic
428	C₂	C₅×#2950	1	1	yes	characteristic
429	C₂	C₅×#3269	1	2	yes	—
430	C₂	C₅×#3349	1	2	yes	—

	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
2. C₂×C₅×#441	C₂	semidirect
5. C₅×#1971	C₂	semidirect
6. C₅×#1943	C₂	semidirect
7. C₅×#1928	C₂	semidirect
9. C₅×#1863	C₂	semidirect
10. C₅×#1776	C₂	semidirect
17. C₅×#467	C₄	semidirect
42. #23030	C₅	direct (N × H)
91. C₂×#441	C₂×C₅	semidirect
94. #1971	C₂×C₅	semidirect
95. #1943	C₂×C₅	semidirect
96. #1928	C₂×C₅	semidirect
98. #1863	C₂×C₅	semidirect
99. #1776	C₂×C₅	semidirect
160. #467	C₄×C₅	semidirect
403. C₅	#23030	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×#467	2
C₂×C₅×#441	2
C₂×C₅×#427	2
C₅×#2362	2
C₅×#1971	2
C₅×#1943	2
C₅×#1928	2
C₅×#1873	2
C₅×#1863	2
C₅×#1776	2
C₅×#1752	2
#23030	5

Subgroups — C5×#23030 #11945750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23030 #11945750