Subgroups — C₅×#21133 #11943853

Order 1280.

890 conjugacy classes of subgroups.

The subgroup lattice has 428 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×#2275	C₂	1	1	yes	maximal, characteristic
4	C₅×#1927	C₂	1	2	yes	maximal, complemented
5	C₅×#1919	C₂	1	2	yes	maximal, complemented
6	C₅×#1877	C₂	1	2	yes	maximal
7	C₅×#1864	C₂	1	2	yes	maximal
8	C₄×C₅×#106	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×#1746	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	2	yes	—
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₄×C₅×SD₁₆	C₄	1	8	yes	complemented
17	C₂×C₅×#106	C₂²	1	2	yes	—
18	C₂×C₅×#106	C₂²	1	1	yes	characteristic
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₅×#103	C₂²	1	1	yes	characteristic
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₂×C₅×#102	C₂²	1	1	yes	characteristic
23	C₂×C₅×#97	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#391	C₂²	1	2	yes	—
26	C₅×#389	C₂²	1	2	yes	—
27	C₅×#387	—	2	2	no	—
28	C₅×#383	—	2	1	no	—
29	C₅×#382	—	2	1	no	—
30	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
34	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
35	C₅×#376	C₂²	1	1	yes	characteristic
36	C₂×C₅×#95	—	2	1	no	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#21133	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	2	no	—
46	C₂³×C₄×C₅	—	2	1	no	—
47	C₂×C₅×SD₁₆	—	2	4	no	—
48	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₄×C₅×Q₈	—	2	2	no	—
53	C₄×C₅×Q₈	C₂×C₄	1	4	yes	complemented
54	C₄×C₅×D₄	—	2	4	no	—
55	C₄×C₅×D₄	—	2	4	no	—
56	C₄×C₅×D₄	—	2	2	no	—
57	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	2	no	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₄²×C₅	—	2	1	no	—
67	C₂×C₄²×C₅	—	2	2	no	—
68	C₂×C₄²×C₅	—	2	1	no	—
69	C₂×C₄²×C₅	—	2	1	no	—
70	C₂×C₄²×C₅	C₂³	1	2	yes	—
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#106	—	2	4	no	—
73	C₅×#106	C₂×C₄	1	4	yes	complemented
74	C₅×#103	—	2	4	no	—
75	C₅×#103	C₂×C₄	1	4	yes	complemented
76	C₅×#102	—	2	4	no	—
77	C₅×#102	C₂×C₄	1	4	yes	—
78	C₅×#97	—	2	2	no	—
79	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
80	C₅×#95	—	2	2	no	—
81	C₅×#95	—	2	1	no	—
82	C₅×#95	—	2	1	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	#2275	C₂×C₅	1	1	yes	characteristic
92	#1927	C₂×C₅	1	2	yes	complemented
93	#1919	C₂×C₅	1	2	yes	complemented
94	#1877	C₂×C₅	1	2	yes	—
95	#1864	C₂×C₅	1	2	yes	—
96	C₄×#106	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	#1746	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	1	no	—
107	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
108	C₂×C₅×D₄	#41	1	4	yes	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	8	no	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	8	2	no	—
117	C₂²×C₄×C₅	—	8	2	no	—
118	C₂²×C₄×C₅	—	8	2	no	—
119	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₅×SD₁₆	—	2	8	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
132	C₅×C₄⋊C₄	—	2	4	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	8	2	no	—
139	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
141	C₅×C₄⋊C₄	#41	1	4	yes	—
142	C₅×C₂²⋊C₄	—	2	8	no	—
143	C₅×C₂²⋊C₄	—	2	4	no	—
144	C₄²×C₅	—	2	4	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	8	1	no	—
148	C₄²×C₅	—	8	1	no	—
149	C₄²×C₅	—	8	2	no	—
150	C₄²×C₅	C₂²×C₄	1	2	yes	—
151	C₄²×C₅	#41	1	2	yes	—
152	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
155	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
156	C₄×SD₁₆	C₄×C₅	1	8	yes	complemented
157	C₂×#106	C₂²×C₅	1	2	yes	—
158	C₂×#106	C₂²×C₅	1	1	yes	characteristic
159	C₂×#103	C₂²×C₅	1	2	yes	—
160	C₂×#103	C₂²×C₅	1	1	yes	characteristic
161	C₂×#102	C₂²×C₅	1	2	yes	—
162	C₂×#102	C₂²×C₅	1	1	yes	characteristic
163	C₂×#97	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
165	#391	C₂²×C₅	1	2	yes	—
166	#389	C₂²×C₅	1	2	yes	—
167	#387	—	2	2	no	—
168	#383	—	2	1	no	—
169	#382	—	2	1	no	—
170	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
172	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	C₄×C₂²⋊C₄	—	2	1	no	—
174	C₄×C₂²⋊C₄	—	2	2	no	—
175	#376	C₂²×C₅	1	1	yes	characteristic
176	C₂×#95	—	2	1	no	—
177	#340	C₂²×C₅	1	2	yes	—
178	#340	C₂²×C₅	1	2	yes	—
179	#340	C₂²×C₅	1	2	yes	—
180	#336	C₂²×C₅	1	2	yes	—
181	#336	C₂²×C₅	1	2	yes	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	2	4	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	4	2	no	—
186	C₂³×C₅	—	4	1	no	—
187	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₅×Q₈	—	2	2	no	—
189	C₅×Q₈	—	2	2	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×D₄	—	2	2	no	—
192	C₅×D₄	—	2	4	no	—
193	C₅×D₄	#117	1	4	yes	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	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	4	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	4	2	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	1	no	—
212	C₂×C₄×C₅	—	4	1	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	—	8	4	no	—
217	C₂×C₄×C₅	—	8	8	no	—
218	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
219	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×#41	1	2	yes	—
222	C₂×C₄×C₅	C₂×#41	1	2	yes	—
223	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
224	C₅×C₈	—	2	2	no	—
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	—	4	2	no	—
227	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
228	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	—	2	1	no	—
231	C₂×SD₁₆	—	2	4	no	—
232	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
233	C₂²×C₈	C₂³×C₅	1	2	yes	—
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
236	C₄×Q₈	—	2	2	no	—
237	C₄×Q₈	C₂×C₄×C₅	1	4	yes	complemented
238	C₄×D₄	—	2	4	no	—
239	C₄×D₄	—	2	4	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	C₂³×C₅	1	2	yes	—
255	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
256	#106	—	2	4	no	—
257	#106	C₂×C₄×C₅	1	4	yes	complemented
258	#103	—	2	4	no	—
259	#103	C₂×C₄×C₅	1	4	yes	complemented
260	#102	—	2	4	no	—
261	#102	C₂×C₄×C₅	1	4	yes	—
262	#97	—	2	2	no	—
263	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
264	#95	—	2	2	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	C₅×D₄	1	1	yes	characteristic
271	#95	C₅×D₄	1	1	yes	characteristic
272	#95	C₅×D₄	1	2	yes	—
273	C₂²×C₅	—	2	4	no	—
274	C₂²×C₅	—	4	4	no	—
275	C₂²×C₅	—	4	4	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂²×C₅	#525	1	2	yes	—
280	C₂²×C₅	#577	1	1	yes	characteristic
281	C₂²×C₅	#577	1	2	yes	—
282	C₂²×C₅	#577	1	1	yes	characteristic
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	—	4	4	no	—
287	C₄×C₅	—	4	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	—	4	2	no	—
291	C₄×C₅	—	8	2	no	—
292	C₄×C₅	C₂×#117	1	1	yes	characteristic
293	C₄×C₅	C₄×#41	1	1	yes	characteristic
294	C₄×C₅	#529	1	2	yes	—
295	C₂⁴	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
303	C₂×D₄	C₅×#41	1	4	yes	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	8	2	no	—
312	C₂²×C₄	—	8	2	no	—
313	C₂²×C₄	—	8	2	no	—
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	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
319	SD₁₆	—	2	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
326	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
335	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
336	C₄⋊C₄	C₅×#41	1	4	yes	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₄²	—	2	4	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	8	1	no	—
343	C₄²	—	8	1	no	—
344	C₄²	—	8	2	no	—
345	C₄²	C₂²×C₄×C₅	1	2	yes	—
346	C₄²	C₅×#41	1	2	yes	—
347	C₂×C₅	—	4	4	no	—
348	C₂×C₅	#2290	1	1	yes	characteristic
349	C₂×C₅	#2949	1	1	yes	characteristic
350	C₂×C₅	#2952	1	1	yes	characteristic
351	C₂×C₅	#3123	1	2	yes	—
352	C₂×C₅	#3125	1	2	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	1	no	—
358	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	4	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	4	no	—
364	D₄	C₅×#117	1	4	yes	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	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	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	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	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	4	no	—
388	C₂×C₄	—	8	8	no	—
389	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
390	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
391	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
392	C₂×C₄	C₂×C₅×#41	1	2	yes	—
393	C₂×C₄	C₂×C₅×#41	1	2	yes	—
394	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₅	#21133	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²	—	2	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
405	C₂²	C₅×#525	1	2	yes	—
406	C₂²	C₅×#577	1	1	yes	characteristic
407	C₂²	C₅×#577	1	2	yes	—
408	C₂²	C₅×#577	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	2	no	—
418	C₄	C₂×C₅×#117	1	1	yes	characteristic
419	C₄	C₄×C₅×#41	1	1	yes	characteristic
420	C₄	C₅×#529	1	2	yes	—
421	C₂	—	4	4	no	—
422	C₂	C₅×#2290	1	1	yes	characteristic
423	C₂	C₅×#2949	1	1	yes	characteristic
424	C₂	C₅×#2952	1	1	yes	characteristic
425	C₂	C₅×#3123	1	2	yes	—
426	C₂	C₅×#3125	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
4. C₅×#1927	C₂	semidirect
5. C₅×#1919	C₂	semidirect
8. C₄×C₅×#106	C₂	semidirect
9. C₅×#1763	C₂	semidirect
11. C₅×#1746	C₂	semidirect
16. C₄×C₅×SD₁₆	C₄	semidirect
42. #21133	C₅	direct (N × H)
53. C₄×C₅×Q₈	C₂×C₄	semidirect
73. C₅×#106	C₂×C₄	semidirect
75. C₅×#103	C₂×C₄	semidirect
79. C₄×C₅×C₈	C₂×C₄	semidirect
90. #2320	C₂×C₅	semidirect
92. #1927	C₂×C₅	semidirect
93. #1919	C₂×C₅	semidirect
96. C₄×#106	C₂×C₅	semidirect
97. #1763	C₂×C₅	semidirect
99. #1746	C₂×C₅	semidirect
156. C₄×SD₁₆	C₄×C₅	semidirect
237. C₄×Q₈	C₂×C₄×C₅	semidirect
257. #106	C₂×C₄×C₅	semidirect
259. #103	C₂×C₄×C₅	semidirect
263. C₄×C₈	C₂×C₄×C₅	semidirect
398. C₅	#21133	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×#2275	2
C₅×#1927	2
C₅×#1919	2
C₅×#1877	2
C₅×#1864	2
C₄×C₅×#106	2
C₅×#1763	2
C₅×#1762	2
C₅×#1746	2
#21133	5

Subgroups — C5×#21133 #11943853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21133 #11943853