Subgroups — C₅×#17943 #11940663

Order 1280.

604 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3108	C₂	1	1	yes	maximal, characteristic
2	C₅×#2966	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1591	C₂	1	2	yes	maximal, complemented
5	C₅×#1590	C₂	1	2	yes	maximal, complemented
6	C₅×#1587	C₂	1	2	yes	maximal, complemented
7	C₅×#1585	C₂	1	2	yes	maximal, complemented
8	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1483	C₂	1	1	yes	maximal, characteristic
11	C₅×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#529	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₅×#483	C₄	1	1	yes	characteristic
15	C₅×#480	C₄	1	1	yes	characteristic
16	C₅×#479	C₄	1	2	yes	—
17	C₅×#464	C₄	1	2	yes	—
18	C₅×#451	C₄	1	1	yes	characteristic
19	C₅×#448	C₄	1	1	yes	characteristic
20	C₅×#446	—	2	1	no	—
21	C₅×#446	—	2	1	no	—
22	C₅×#446	C₂²	1	2	yes	—
23	C₅×#446	C₂²	1	2	yes	—
24	C₅×#446	C₂²	1	1	yes	characteristic
25	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
26	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
27	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
28	C₅×#436	C₂²	1	1	yes	characteristic
29	C₅×#435	—	2	1	no	—
30	C₅×C₈×D₄	—	2	1	no	—
31	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
32	C₅×#433	—	2	1	no	—
33	C₅×#432	C₂²	1	1	yes	characteristic
34	C₅×#431	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₄⋊C₈	—	2	1	no	—
36	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₅×#405	—	2	1	no	—
38	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₅×#97	—	2	1	no	—
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#335	C₂²	1	2	yes	—
42	C₅×#334	C₂²	1	2	yes	—
43	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₅×D₄⋊C₈	C₂²	1	2	yes	—
47	C₅×#322	C₂²	1	2	yes	—
48	C₅×C₈²	C₂²	1	2	yes	—
49	#17943	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂²×C₅×C₈	—	2	1	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
59	C₅×#126	—	2	1	no	—
60	C₅×#125	C₂×C₄	1	1	yes	characteristic
61	C₅×#124	C₂×C₄	1	1	yes	characteristic
62	C₅×#123	—	2	1	no	—
63	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
64	C₅×#121	C₂×C₄	1	1	yes	characteristic
65	C₄×C₅×Q₈	—	2	1	no	—
66	C₄×C₅×Q₈	—	2	1	no	—
67	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
68	C₄×C₅×Q₈	C₂³	1	2	yes	—
69	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₅×#117	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	C₂×C₄	1	2	yes	—
78	C₅×#106	C₂×C₄	1	2	yes	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
85	C₅×C₄⋊C₈	C₂³	1	2	yes	—
86	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×#103	C₂×C₄	1	2	yes	—
89	C₅×#103	C₂×C₄	1	2	yes	—
90	C₅×#103	C₂×C₄	1	2	yes	—
91	C₅×#102	C₂×C₄	1	2	yes	—
92	C₅×C₂²⋊C₈	—	2	1	no	—
93	C₅×C₂²⋊C₈	—	2	1	no	—
94	C₅×C₂²⋊C₈	—	2	1	no	—
95	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₅×#97	—	2	2	no	—
98	C₅×#97	—	2	2	no	—
99	C₅×#97	—	2	1	no	—
100	C₅×#97	—	2	1	no	—
101	C₅×#97	—	2	1	no	—
102	C₄×C₅×C₈	—	2	1	no	—
103	C₄×C₅×C₈	D₄	1	1	yes	characteristic
104	C₄×C₅×C₈	D₄	1	1	yes	characteristic
105	C₄×C₅×C₈	C₂³	1	2	yes	—
106	C₄×C₅×C₈	C₂³	1	2	yes	—
107	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	#3108	C₂×C₅	1	1	yes	characteristic
110	#2966	C₂×C₅	1	1	yes	characteristic
111	C₂×#446	C₂×C₅	1	1	yes	characteristic, complemented
112	#1591	C₂×C₅	1	2	yes	complemented
113	#1590	C₂×C₅	1	2	yes	complemented
114	#1587	C₂×C₅	1	2	yes	complemented
115	#1585	C₂×C₅	1	2	yes	complemented
116	#1573	C₂×C₅	1	1	yes	characteristic, complemented
117	#1491	C₂×C₅	1	1	yes	characteristic, complemented
118	#1483	C₂×C₅	1	1	yes	characteristic
119	C₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×C₅×Q₈	—	2	1	no	—
121	C₂×C₅×Q₈	—	4	2	no	—
122	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
123	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₅×D₄	—	2	1	no	—
125	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	#41	1	1	yes	characteristic
132	C₅×Q₁₆	—	4	2	no	—
133	C₅×SD₁₆	—	4	2	no	—
134	C₅×M₁₆	—	2	4	no	—
135	C₅×M₁₆	—	4	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	4	1	no	—
142	C₂×C₅×C₈	—	4	2	no	—
143	C₂×C₅×C₈	—	4	2	no	—
144	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
158	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
160	C₅×C₂²⋊C₄	—	2	1	no	—
161	C₅×C₂²⋊C₄	—	2	1	no	—
162	C₅×C₂²⋊C₄	—	2	1	no	—
163	C₅×C₂²⋊C₄	—	2	1	no	—
164	C₅×C₂²⋊C₄	—	2	1	no	—
165	C₄²×C₅	—	2	2	no	—
166	C₄²×C₅	—	2	2	no	—
167	C₄²×C₅	—	2	1	no	—
168	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₅	#41	1	1	yes	characteristic
171	C₄²×C₅	C₂⁴	1	1	yes	characteristic
172	#529	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
174	#483	C₄×C₅	1	1	yes	characteristic
175	#480	C₄×C₅	1	1	yes	characteristic
176	#479	C₄×C₅	1	2	yes	—
177	#464	C₄×C₅	1	2	yes	—
178	#451	C₄×C₅	1	1	yes	characteristic
179	#448	C₄×C₅	1	1	yes	characteristic
180	#446	—	2	1	no	—
181	#446	—	2	1	no	—
182	#446	C₂²×C₅	1	2	yes	—
183	#446	C₂²×C₅	1	2	yes	—
184	#446	C₂²×C₅	1	1	yes	characteristic
185	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
186	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
187	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
188	#436	C₂²×C₅	1	1	yes	characteristic
189	#435	—	2	1	no	—
190	C₈×D₄	—	2	1	no	—
191	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
192	#433	—	2	1	no	—
193	#432	C₂²×C₅	1	1	yes	characteristic
194	#431	C₂²×C₅	1	1	yes	characteristic
195	C₂×C₄⋊C₈	—	2	1	no	—
196	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
197	#405	—	2	1	no	—
198	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
199	C₂×#97	—	2	1	no	—
200	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
201	#335	C₂²×C₅	1	2	yes	—
202	#334	C₂²×C₅	1	2	yes	—
203	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
204	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
205	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
206	D₄⋊C₈	C₂²×C₅	1	2	yes	—
207	#322	C₂²×C₅	1	2	yes	—
208	C₈²	C₂²×C₅	1	2	yes	—
209	C₂³×C₅	—	2	1	no	—
210	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
211	C₅×Q₈	—	2	2	no	—
212	C₅×Q₈	—	2	2	no	—
213	C₅×Q₈	—	2	2	no	—
214	C₅×Q₈	—	4	2	no	—
215	C₅×D₄	—	2	2	no	—
216	C₅×D₄	—	4	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
236	C₅×C₈	—	2	4	no	—
237	C₅×C₈	—	2	2	no	—
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	2	1	no	—
240	C₅×C₈	—	2	1	no	—
241	C₅×C₈	—	2	1	no	—
242	C₅×C₈	—	4	1	no	—
243	C₅×C₈	—	4	1	no	—
244	C₅×C₈	—	4	2	no	—
245	C₅×C₈	#137	1	2	yes	—
246	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
247	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
248	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
254	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
255	#126	—	2	1	no	—
256	#125	C₂×C₄×C₅	1	1	yes	characteristic
257	#124	C₂×C₄×C₅	1	1	yes	characteristic
258	#123	—	2	1	no	—
259	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
260	#121	C₂×C₄×C₅	1	1	yes	characteristic
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
264	C₄×Q₈	C₂³×C₅	1	2	yes	—
265	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
268	#117	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
273	#107	C₂×C₄×C₅	1	2	yes	—
274	#106	C₂×C₄×C₅	1	2	yes	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
281	C₄⋊C₈	C₂³×C₅	1	2	yes	—
282	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
283	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
284	#103	C₂×C₄×C₅	1	2	yes	—
285	#103	C₂×C₄×C₅	1	2	yes	—
286	#103	C₂×C₄×C₅	1	2	yes	—
287	#102	C₂×C₄×C₅	1	2	yes	—
288	C₂²⋊C₈	—	2	1	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
292	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
293	#97	—	2	2	no	—
294	#97	—	2	2	no	—
295	#97	—	2	1	no	—
296	#97	—	2	1	no	—
297	#97	—	2	1	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	C₅×D₄	1	1	yes	characteristic
300	C₄×C₈	C₅×D₄	1	1	yes	characteristic
301	C₄×C₈	C₂³×C₅	1	2	yes	—
302	C₄×C₈	C₂³×C₅	1	2	yes	—
303	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
304	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
305	C₂²×C₅	—	2	1	no	—
306	C₂²×C₅	—	2	1	no	—
307	C₂²×C₅	—	4	1	no	—
308	C₂²×C₅	—	4	1	no	—
309	C₂²×C₅	—	4	1	no	—
310	C₂²×C₅	#443	1	2	yes	—
311	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	2	1	no	—
314	C₄×C₅	—	2	1	no	—
315	C₄×C₅	—	2	1	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	1	no	—
318	C₄×C₅	—	4	1	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	4	1	no	—
321	C₄×C₅	#568	1	2	yes	—
322	C₄×C₅	C₂×#137	1	1	yes	characteristic
323	C₄×C₅	#575	1	1	yes	characteristic
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
327	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₅×#41	1	1	yes	characteristic
336	Q₁₆	—	4	2	no	—
337	SD₁₆	—	4	2	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	4	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
349	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
350	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
351	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
362	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
373	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
374	C₄²	C₅×#41	1	1	yes	characteristic
375	C₄²	C₂⁴×C₅	1	1	yes	characteristic
376	C₂×C₅	—	2	2	no	—
377	C₂×C₅	—	8	1	no	—
378	C₂×C₅	#2930	1	1	yes	characteristic
379	C₂×C₅	C₄×#137	1	1	yes	characteristic
380	C₂×C₅	C₂×#443	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	4	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
403	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
404	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
405	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
407	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
408	C₈	—	2	4	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	2	no	—
417	C₈	C₅×#137	1	2	yes	—
418	C₅	#17943	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	C₅×#443	1	2	yes	—
425	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	1	no	—
435	C₄	C₅×#568	1	2	yes	—
436	C₄	C₂×C₅×#137	1	1	yes	characteristic
437	C₄	C₅×#575	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	8	1	no	—
440	C₂	C₅×#2930	1	1	yes	characteristic
441	C₂	C₄×C₅×#137	1	1	yes	characteristic
442	C₂	C₂×C₅×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#121	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#446	C₂	semidirect
4. C₅×#1591	C₂	semidirect
5. C₅×#1590	C₂	semidirect
6. C₅×#1587	C₂	semidirect
7. C₅×#1585	C₂	semidirect
8. C₅×#1573	C₂	semidirect
9. C₅×#1491	C₂	semidirect
11. C₅×C₈×M₁₆	C₂	semidirect
49. #17943	C₅	direct (N × H)
111. C₂×#446	C₂×C₅	semidirect
112. #1591	C₂×C₅	semidirect
113. #1590	C₂×C₅	semidirect
114. #1587	C₂×C₅	semidirect
115. #1585	C₂×C₅	semidirect
116. #1573	C₂×C₅	semidirect
117. #1491	C₂×C₅	semidirect
119. C₈×M₁₆	C₂×C₅	semidirect
418. C₅	#17943	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3108	2
C₅×#2966	2
C₂×C₅×#446	2
C₅×#1591	2
C₅×#1590	2
C₅×#1587	2
C₅×#1585	2
C₅×#1573	2
C₅×#1491	2
C₅×#1483	2
C₅×C₈×M₁₆	2
#17943	5

Subgroups — C5×#17943 #11940663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17943 #11940663