Subgroups — C₅×#21285 #11944005

Order 1280.

814 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#2320	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2319	C₂	1	1	yes	maximal, characteristic
4	C₅×#1973	C₂	1	2	yes	maximal
5	C₅×#1944	C₂	1	2	yes	maximal, complemented
6	C₅×#1934	C₂	1	2	yes	maximal
7	C₅×#1933	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1763	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1762	C₂	1	1	yes	maximal, characteristic
11	C₅×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₄×C₅×SD₁₆	C₄	1	8	yes	complemented
16	C₂×C₅×#107	C₂²	1	2	yes	—
17	C₂×C₅×#106	C₂²	1	1	yes	characteristic
18	C₂×C₅×#103	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	1	yes	characteristic
20	C₂×C₅×#102	C₂²	1	2	yes	—
21	C₂×C₅×#102	C₂²	1	1	yes	characteristic
22	C₂×C₅×#97	C₂²	1	1	yes	characteristic
23	C₂×C₅×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₅×#391	C₂²	1	2	yes	—
27	C₅×#390	C₂²	1	2	yes	—
28	C₅×#389	C₂²	1	2	yes	—
29	C₅×#389	C₂²	1	2	yes	—
30	C₅×#388	—	2	2	no	—
31	C₅×#387	—	2	2	no	—
32	C₅×#383	—	2	1	no	—
33	C₅×#382	—	2	1	no	—
34	C₅×#381	—	2	1	no	—
35	C₅×#380	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×#376	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	#21285	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂×C₅×SD₁₆	—	2	4	no	—
47	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₄×C₅×Q₈	—	2	2	no	—
52	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
53	C₄×C₅×D₄	—	2	2	no	—
54	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	2	no	—
57	C₂×C₅×C₄⋊C₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	—	2	1	no	—
67	C₂×C₄²×C₅	—	2	1	no	—
68	C₂×C₄²×C₅	C₂³	1	2	yes	—
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#107	—	2	4	no	—
71	C₅×#106	C₂×C₄	1	4	yes	—
72	C₅×#103	—	2	4	no	—
73	C₅×#103	C₂×C₄	1	4	yes	—
74	C₅×#102	—	2	4	no	—
75	C₅×#102	C₂×C₄	1	4	yes	—
76	C₅×#97	—	2	4	no	—
77	C₅×#97	—	2	2	no	—
78	C₄×C₅×C₈	—	2	4	no	—
79	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
80	C₅×#95	—	2	1	no	—
81	C₅×#95	—	2	1	no	—
82	C₅×#95	—	2	2	no	—
83	C₅×#95	—	2	2	no	—
84	C₅×#95	—	2	2	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	D₄	1	1	yes	characteristic
87	C₅×#95	D₄	1	1	yes	characteristic
88	C₅×#95	D₄	1	2	yes	—
89	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic
90	#2320	C₂×C₅	1	1	yes	characteristic, complemented
91	#2319	C₂×C₅	1	1	yes	characteristic
92	#1973	C₂×C₅	1	2	yes	—
93	#1944	C₂×C₅	1	2	yes	complemented
94	#1934	C₂×C₅	1	2	yes	—
95	#1933	C₂×C₅	1	2	yes	complemented
96	C₄×#107	C₂×C₅	1	1	yes	characteristic, complemented
97	#1763	C₂×C₅	1	1	yes	characteristic, complemented
98	#1762	C₂×C₅	1	1	yes	characteristic
99	#1726	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂⁴×C₅	—	2	1	no	—
101	C₂×C₅×Q₈	—	2	1	no	—
102	C₂×C₅×Q₈	—	2	2	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	2	2	no	—
107	C₂×C₅×D₄	—	2	1	no	—
108	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
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	4	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	8	2	no	—
116	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₅×SD₁₆	—	2	8	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
127	C₂×C₅×C₈	#41	1	4	yes	—
128	C₂×C₅×C₈	#41	1	4	yes	—
129	C₅×C₄⋊C₄	—	2	4	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	8	2	no	—
137	C₅×C₄⋊C₄	—	8	2	no	—
138	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
139	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₅×C₂²⋊C₄	—	2	4	no	—
141	C₅×C₂²⋊C₄	—	8	2	no	—
142	C₅×C₂²⋊C₄	—	8	2	no	—
143	C₄²×C₅	—	2	4	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	8	1	no	—
147	C₄²×C₅	—	8	1	no	—
148	C₄²×C₅	C₂²×C₄	1	2	yes	—
149	C₄²×C₅	#41	1	2	yes	—
150	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
153	C₄×SD₁₆	C₄×C₅	1	8	yes	complemented
154	C₂×#107	C₂²×C₅	1	2	yes	—
155	C₂×#106	C₂²×C₅	1	1	yes	characteristic
156	C₂×#103	C₂²×C₅	1	2	yes	—
157	C₂×#103	C₂²×C₅	1	1	yes	characteristic
158	C₂×#102	C₂²×C₅	1	2	yes	—
159	C₂×#102	C₂²×C₅	1	1	yes	characteristic
160	C₂×#97	C₂²×C₅	1	2	yes	—
161	C₂×#97	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
163	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
164	#391	C₂²×C₅	1	2	yes	—
165	#390	C₂²×C₅	1	2	yes	—
166	#389	C₂²×C₅	1	2	yes	—
167	#389	C₂²×C₅	1	2	yes	—
168	#388	—	2	2	no	—
169	#387	—	2	2	no	—
170	#383	—	2	1	no	—
171	#382	—	2	1	no	—
172	#381	—	2	1	no	—
173	#380	—	2	1	no	—
174	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	#376	C₂²×C₅	1	1	yes	characteristic
177	#340	C₂²×C₅	1	2	yes	—
178	#340	C₂²×C₅	1	2	yes	—
179	#340	C₂²×C₅	1	2	yes	—
180	C₂³×C₅	—	2	2	no	—
181	C₂³×C₅	—	4	2	no	—
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₅×Q₈	—	2	2	no	—
187	C₅×Q₈	—	2	2	no	—
188	C₅×Q₈	—	4	2	no	—
189	C₅×D₄	—	2	2	no	—
190	C₅×D₄	—	2	2	no	—
191	C₅×D₄	—	4	2	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	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	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	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	—	8	4	no	—
215	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
216	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
217	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×#41	1	2	yes	—
219	C₂×C₄×C₅	C₂×#41	1	2	yes	—
220	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
221	C₅×C₈	—	2	2	no	—
222	C₅×C₈	—	2	4	no	—
223	C₅×C₈	#117	1	4	yes	—
224	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
225	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂×SD₁₆	—	2	4	no	—
228	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
229	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₅	1	2	yes	—
231	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
232	C₄×Q₈	—	2	2	no	—
233	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	C₂³×C₅	1	2	yes	—
250	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
251	#107	—	2	4	no	—
252	#106	C₂×C₄×C₅	1	4	yes	—
253	#103	—	2	4	no	—
254	#103	C₂×C₄×C₅	1	4	yes	—
255	#102	—	2	4	no	—
256	#102	C₂×C₄×C₅	1	4	yes	—
257	#97	—	2	4	no	—
258	#97	—	2	2	no	—
259	C₄×C₈	—	2	4	no	—
260	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
261	#95	—	2	1	no	—
262	#95	—	2	1	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	C₅×D₄	1	1	yes	characteristic
268	#95	C₅×D₄	1	1	yes	characteristic
269	#95	C₅×D₄	1	2	yes	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	4	2	no	—
272	C₂²×C₅	—	4	2	no	—
273	C₂²×C₅	—	8	2	no	—
274	C₂²×C₅	—	8	2	no	—
275	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂²×C₅	#532	1	2	yes	—
277	C₂²×C₅	#576	1	1	yes	characteristic
278	C₂²×C₅	#577	1	2	yes	—
279	C₂²×C₅	#578	1	1	yes	characteristic
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	—	4	2	no	—
284	C₄×C₅	—	4	2	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	—	4	2	no	—
287	C₄×C₅	—	8	2	no	—
288	C₄×C₅	—	8	2	no	—
289	C₄×C₅	C₂×#117	1	1	yes	characteristic
290	C₄×C₅	C₄×#41	1	1	yes	characteristic
291	C₄×C₅	#529	1	2	yes	—
292	C₂⁴	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
309	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
310	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
313	SD₁₆	—	2	8	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
318	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
319	C₂×C₈	C₅×#41	1	4	yes	—
320	C₂×C₈	C₅×#41	1	4	yes	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	8	2	no	—
329	C₄⋊C₄	—	8	2	no	—
330	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
331	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	8	2	no	—
334	C₂²⋊C₄	—	8	2	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	8	1	no	—
339	C₄²	—	8	1	no	—
340	C₄²	C₂²×C₄×C₅	1	2	yes	—
341	C₄²	C₅×#41	1	2	yes	—
342	C₂×C₅	—	8	2	no	—
343	C₂×C₅	#2293	1	1	yes	characteristic
344	C₂×C₅	#2949	1	1	yes	characteristic
345	C₂×C₅	#2951	1	1	yes	characteristic
346	C₂×C₅	#3178	1	2	yes	—
347	C₂×C₅	#3179	1	2	yes	—
348	C₂³	—	2	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	1	no	—
353	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	4	no	—
383	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
384	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
385	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
386	C₂×C₄	C₂×C₅×#41	1	2	yes	—
387	C₂×C₄	C₂×C₅×#41	1	2	yes	—
388	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	4	no	—
391	C₈	C₅×#117	1	4	yes	—
392	C₅	#21285	1	1	yes	characteristic, direct product factor, Sylow
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
399	C₂²	C₅×#532	1	2	yes	—
400	C₂²	C₅×#576	1	1	yes	characteristic
401	C₂²	C₅×#577	1	2	yes	—
402	C₂²	C₅×#578	1	1	yes	characteristic
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	2	no	—
412	C₄	C₂×C₅×#117	1	1	yes	characteristic
413	C₄	C₄×C₅×#41	1	1	yes	characteristic
414	C₄	C₅×#529	1	2	yes	—
415	C₂	—	8	2	no	—
416	C₂	C₅×#2293	1	1	yes	characteristic
417	C₂	C₅×#2949	1	1	yes	characteristic
418	C₂	C₅×#2951	1	1	yes	characteristic
419	C₂	C₅×#3178	1	2	yes	—
420	C₂	C₅×#3179	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	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×#2320	C₂	semidirect
5. C₅×#1944	C₂	semidirect
7. C₅×#1933	C₂	semidirect
8. C₄×C₅×#107	C₂	semidirect
9. C₅×#1763	C₂	semidirect
11. C₅×#1726	C₂	semidirect
15. C₄×C₅×SD₁₆	C₄	semidirect
42. #21285	C₅	direct (N × H)
90. #2320	C₂×C₅	semidirect
93. #1944	C₂×C₅	semidirect
95. #1933	C₂×C₅	semidirect
96. C₄×#107	C₂×C₅	semidirect
97. #1763	C₂×C₅	semidirect
99. #1726	C₂×C₅	semidirect
153. C₄×SD₁₆	C₄×C₅	semidirect
392. C₅	#21285	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×C₄×C₅×SD₁₆	2
C₅×#2320	2
C₅×#2319	2
C₅×#1973	2
C₅×#1944	2
C₅×#1934	2
C₅×#1933	2
C₄×C₅×#107	2
C₅×#1763	2
C₅×#1762	2
C₅×#1726	2
#21285	5

Subgroups — C5×#21285 #11944005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21285 #11944005