Subgroups — C₅×#21696 #11944416

Order 1280.

1110 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×C₅×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#440	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic
5	C₅×#2326	C₂	1	2	yes	maximal, complemented
6	C₅×#1973	C₂	1	2	yes	maximal, complemented
7	C₅×#1970	C₂	1	1	yes	maximal, characteristic
8	C₅×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1959	C₂	1	2	yes	maximal, complemented
10	C₅×#1845	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#124	C₂²	1	2	yes	—
16	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
17	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₅×#495	C₄	1	8	yes	complemented
19	C₅×#440	—	2	8	no	—
20	C₄×C₅×Q₁₆	—	2	4	no	—
21	C₄×C₅×D₈	—	2	4	no	—
22	C₂×C₅×#107	C₂²	1	1	yes	characteristic
23	C₂×C₅×#107	C₂²	1	1	yes	characteristic
24	C₂×C₅×#107	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#103	C₂²	1	2	yes	—
27	C₂×C₅×#102	C₂²	1	2	yes	—
28	C₂×C₅×#102	C₂²	1	2	yes	—
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	C₂²	1	1	yes	characteristic
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#391	C₂²	1	2	yes	—
36	C₅×#390	C₂²	1	2	yes	—
37	C₅×#388	—	2	4	no	—
38	C₅×#385	—	2	4	no	—
39	C₅×#384	C₂²	1	2	yes	—
40	C₅×#376	C₂²	1	1	yes	characteristic
41	#21696	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₅×Q₈	C₂³	1	2	yes	—
43	C₂²×C₅×D₄	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	—	2	2	no	—
45	C₂×C₅×Q₁₆	—	2	2	no	—
46	C₂×C₅×Q₁₆	—	2	2	no	—
47	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
48	C₂×C₅×SD₁₆	—	2	4	no	—
49	C₂×C₅×SD₁₆	—	2	4	no	—
50	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
51	C₂×C₅×D₈	—	2	2	no	—
52	C₂×C₅×D₈	—	2	2	no	—
53	C₂×C₅×D₈	C₂×C₄	1	4	yes	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₅×#124	—	2	4	no	—
59	C₅×#124	C₂×C₄	1	8	yes	complemented
60	C₄×C₅×Q₈	—	2	4	no	—
61	C₄×C₅×Q₈	—	2	4	no	—
62	C₄×C₅×D₄	—	2	4	no	—
63	C₄×C₅×D₄	—	2	4	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	4	no	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	—	2	2	no	—
76	C₅×#107	—	2	2	no	—
77	C₅×#107	—	2	4	no	—
78	C₅×#103	—	2	4	no	—
79	C₅×#103	—	2	4	no	—
80	C₅×#102	—	2	4	no	—
81	C₅×#102	—	2	4	no	—
82	C₅×#97	—	2	2	no	—
83	C₅×#97	—	2	2	no	—
84	C₅×#97	D₄	1	4	yes	—
85	C₄×C₅×C₈	—	2	2	no	—
86	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
87	C₄×C₅×C₈	D₄	1	4	yes	—
88	C₅×#95	—	2	4	no	—
89	C₅×#95	D₄	1	2	yes	—
90	C₅×#95	D₄	1	2	yes	—
91	C₂×#495	C₂×C₅	1	1	yes	characteristic
92	C₂×#440	C₂×C₅	1	2	yes	complemented
93	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic
95	#2326	C₂×C₅	1	2	yes	complemented
96	#1973	C₂×C₅	1	2	yes	complemented
97	#1970	C₂×C₅	1	1	yes	characteristic
98	#1969	C₂×C₅	1	1	yes	characteristic, complemented
99	#1959	C₂×C₅	1	2	yes	complemented
100	#1845	C₂×C₅	1	1	yes	characteristic, complemented
101	#1726	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂⁴×C₅	—	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	—	2	2	no	—
108	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	4	4	no	—
119	C₂²×C₄×C₅	—	8	4	no	—
120	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₅×Q₁₆	—	2	8	no	—
126	C₅×SD₁₆	—	2	16	no	—
127	C₅×D₈	—	2	8	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	C₂×D₄	1	2	yes	—
136	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
137	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₅×C₈	#41	1	2	yes	—
139	C₂×C₅×C₈	#41	1	2	yes	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	4	4	no	—
145	C₅×C₄⋊C₄	—	8	4	no	—
146	C₅×C₂²⋊C₄	—	2	16	no	—
147	C₅×C₂²⋊C₄	—	4	4	no	—
148	C₅×C₂²⋊C₄	—	8	4	no	—
149	C₄²×C₅	—	2	1	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄²×C₅	—	4	4	no	—
152	C₄²×C₅	C₂²×C₄	1	2	yes	—
153	C₄²×C₅	C₂×D₄	1	2	yes	—
154	C₄²×C₅	C₂×D₄	1	2	yes	—
155	C₄²×C₅	#41	1	2	yes	—
156	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
157	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
158	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×#124	C₂²×C₅	1	2	yes	—
160	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
161	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
162	#495	C₄×C₅	1	8	yes	complemented
163	#440	—	2	8	no	—
164	C₄×Q₁₆	—	2	4	no	—
165	C₄×D₈	—	2	4	no	—
166	C₂×#107	C₂²×C₅	1	1	yes	characteristic
167	C₂×#107	C₂²×C₅	1	1	yes	characteristic
168	C₂×#107	C₂²×C₅	1	2	yes	—
169	C₂×#103	C₂²×C₅	1	2	yes	—
170	C₂×#103	C₂²×C₅	1	2	yes	—
171	C₂×#102	C₂²×C₅	1	2	yes	—
172	C₂×#102	C₂²×C₅	1	2	yes	—
173	C₂×#97	C₂²×C₅	1	1	yes	characteristic
174	C₂×#97	C₂²×C₅	1	1	yes	characteristic
175	C₂×#97	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
179	#391	C₂²×C₅	1	2	yes	—
180	#390	C₂²×C₅	1	2	yes	—
181	#388	—	2	4	no	—
182	#385	—	2	4	no	—
183	#384	C₂²×C₅	1	2	yes	—
184	#376	C₂²×C₅	1	1	yes	characteristic
185	C₂³×C₅	—	2	4	no	—
186	C₂³×C₅	—	4	2	no	—
187	C₂³×C₅	—	4	2	no	—
188	C₂³×C₅	—	4	4	no	—
189	C₂³×C₅	—	4	4	no	—
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	C₅×D₄	—	2	4	no	—
196	C₅×D₄	—	2	4	no	—
197	C₅×D₄	—	4	2	no	—
198	C₅×D₄	—	4	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	4	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	4	no	—
212	C₂×C₄×C₅	—	4	4	no	—
213	C₂×C₄×C₅	—	8	8	no	—
214	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
215	C₂×C₄×C₅	#127	1	2	yes	—
216	C₂×C₄×C₅	#127	1	2	yes	—
217	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	2	2	no	—
225	C₅×C₈	C₄×D₄	1	4	yes	—
226	C₅×C₈	C₄×D₄	1	4	yes	—
227	C₂²×Q₈	C₂³×C₅	1	2	yes	—
228	C₂²×D₄	C₂³×C₅	1	2	yes	—
229	C₂³×C₄	—	2	2	no	—
230	C₂×Q₁₆	—	2	2	no	—
231	C₂×Q₁₆	—	2	2	no	—
232	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
233	C₂×SD₁₆	—	2	4	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
236	C₂×D₈	—	2	2	no	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	C₂×C₄×C₅	1	4	yes	—
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×C₈	C₂³×C₅	1	1	yes	characteristic
243	#124	—	2	4	no	—
244	#124	C₂×C₄×C₅	1	8	yes	complemented
245	C₄×Q₈	—	2	4	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	4	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
260	#107	—	2	2	no	—
261	#107	—	2	2	no	—
262	#107	—	2	4	no	—
263	#103	—	2	4	no	—
264	#103	—	2	4	no	—
265	#102	—	2	4	no	—
266	#102	—	2	4	no	—
267	#97	—	2	2	no	—
268	#97	—	2	2	no	—
269	#97	C₅×D₄	1	4	yes	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
272	C₄×C₈	C₅×D₄	1	4	yes	—
273	#95	—	2	4	no	—
274	#95	C₅×D₄	1	2	yes	—
275	#95	C₅×D₄	1	2	yes	—
276	C₂²×C₅	—	4	4	no	—
277	C₂²×C₅	—	4	8	no	—
278	C₂²×C₅	—	8	2	no	—
279	C₂²×C₅	—	8	2	no	—
280	C₂²×C₅	—	8	4	no	—
281	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂²×C₅	C₂×#127	1	1	yes	characteristic
283	C₂²×C₅	#532	1	1	yes	characteristic
284	C₂²×C₅	#576	1	2	yes	—
285	C₂²×C₅	#578	1	2	yes	—
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	2	4	no	—
289	C₄×C₅	—	4	4	no	—
290	C₄×C₅	—	4	2	no	—
291	C₄×C₅	—	8	2	no	—
292	C₄×C₅	—	8	2	no	—
293	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
294	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
295	C₄×C₅	#532	1	1	yes	characteristic
296	C₄×C₅	#532	1	1	yes	characteristic
297	C₂⁴	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
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	C₂²×C₄×C₅	1	4	yes	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	—	8	4	no	—
315	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
316	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
317	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
320	Q₁₆	—	2	8	no	—
321	SD₁₆	—	2	16	no	—
322	D₈	—	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	C₂²×C₄×C₅	1	2	yes	—
328	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
329	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
330	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
331	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
332	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
333	C₂×C₈	C₅×#41	1	2	yes	—
334	C₂×C₈	C₅×#41	1	2	yes	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	8	4	no	—
341	C₂²⋊C₄	—	2	16	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	8	4	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	4	no	—
347	C₄²	C₂²×C₄×C₅	1	2	yes	—
348	C₄²	C₂×C₅×D₄	1	2	yes	—
349	C₄²	C₂×C₅×D₄	1	2	yes	—
350	C₄²	C₅×#41	1	2	yes	—
351	C₂×C₅	—	8	4	no	—
352	C₂×C₅	C₄×#127	1	1	yes	characteristic
353	C₂×C₅	#2951	1	2	yes	—
354	C₂×C₅	#3155	1	1	yes	characteristic
355	C₂×C₅	#3156	1	1	yes	characteristic
356	C₂×C₅	#3175	1	2	yes	—
357	C₂³	—	2	4	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	4	no	—
362	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	D₄	—	2	4	no	—
368	D₄	—	2	4	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	8	8	no	—
386	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
387	C₂×C₄	C₅×#127	1	2	yes	—
388	C₂×C₄	C₅×#127	1	2	yes	—
389	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
393	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
394	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	C₄×C₅×D₄	1	4	yes	—
398	C₈	C₄×C₅×D₄	1	4	yes	—
399	C₅	#21696	1	1	yes	characteristic, direct product factor, Sylow
400	C₂²	—	4	4	no	—
401	C₂²	—	4	8	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	4	no	—
405	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
406	C₂²	C₂×C₅×#127	1	1	yes	characteristic
407	C₂²	C₅×#532	1	1	yes	characteristic
408	C₂²	C₅×#576	1	2	yes	—
409	C₂²	C₅×#578	1	2	yes	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	4	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
418	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
419	C₄	C₅×#532	1	1	yes	characteristic
420	C₄	C₅×#532	1	1	yes	characteristic
421	C₂	—	8	4	no	—
422	C₂	C₄×C₅×#127	1	1	yes	characteristic
423	C₂	C₅×#2951	1	2	yes	—
424	C₂	C₅×#3155	1	1	yes	characteristic
425	C₂	C₅×#3156	1	1	yes	characteristic
426	C₂	C₅×#3175	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×D₈	C₂²
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. C₂×C₅×#440	C₂	semidirect
3. C₂×C₄×C₅×Q₁₆	C₂	semidirect
5. C₅×#2326	C₂	semidirect
6. C₅×#1973	C₂	semidirect
8. C₅×#1969	C₂	semidirect
9. C₅×#1959	C₂	semidirect
10. C₅×#1845	C₂	semidirect
11. C₅×#1726	C₂	semidirect
18. C₅×#495	C₄	semidirect
41. #21696	C₅	direct (N × H)
47. C₂×C₅×Q₁₆	C₂×C₄	semidirect
50. C₂×C₅×SD₁₆	C₂×C₄	semidirect
59. C₅×#124	C₂×C₄	semidirect
86. C₄×C₅×C₈	C₂×C₄	semidirect
92. C₂×#440	C₂×C₅	semidirect
93. C₂×C₄×Q₁₆	C₂×C₅	semidirect
95. #2326	C₂×C₅	semidirect
96. #1973	C₂×C₅	semidirect
98. #1969	C₂×C₅	semidirect
99. #1959	C₂×C₅	semidirect
100. #1845	C₂×C₅	semidirect
101. #1726	C₂×C₅	semidirect
162. #495	C₄×C₅	semidirect
232. C₂×Q₁₆	C₂×C₄×C₅	semidirect
235. C₂×SD₁₆	C₂×C₄×C₅	semidirect
244. #124	C₂×C₄×C₅	semidirect
271. C₄×C₈	C₂×C₄×C₅	semidirect
399. C₅	#21696	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×#495	2
C₂×C₅×#440	2
C₂×C₄×C₅×Q₁₆	2
C₂×C₄×C₅×D₈	2
C₅×#2326	2
C₅×#1973	2
C₅×#1970	2
C₅×#1969	2
C₅×#1959	2
C₅×#1845	2
C₅×#1726	2
#21696	5

Subgroups — C5×#21696 #11944416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21696 #11944416