Subgroups — C₅×#18025 #11940745

Order 1280.

630 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3106	C₂	1	1	yes	maximal, characteristic
2	C₅×#2991	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2979	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1594	C₂	1	2	yes	maximal, complemented
5	C₅×#1583	C₂	1	2	yes	maximal, complemented
6	C₅×#1581	C₂	1	2	yes	maximal, complemented
7	C₅×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₅×#482	C₄	1	2	yes	—
15	C₅×#477	C₄	1	1	yes	characteristic
16	C₅×#476	C₄	1	1	yes	characteristic
17	C₅×#460	C₄	1	1	yes	characteristic
18	C₅×#459	C₄	1	1	yes	characteristic
19	C₅×#449	C₄	1	2	yes	—
20	C₅×C₈×Q₈	C₂²	1	2	yes	—
21	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₅×D₈	C₂²	1	2	yes	—
23	C₅×#436	—	2	1	no	—
24	C₅×#436	—	2	2	no	—
25	C₅×#436	C₂²	1	2	yes	—
26	C₅×#436	C₂²	1	2	yes	—
27	C₅×C₈×D₄	—	2	1	no	—
28	C₅×C₈×D₄	C₂²	1	2	yes	—
29	C₅×#431	—	2	1	no	—
30	C₅×#431	C₂²	1	1	yes	characteristic
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#431	C₂²	1	1	yes	characteristic
33	C₅×#423	—	2	1	no	—
34	C₅×#423	C₂²	1	1	yes	characteristic
35	C₅×#408	—	2	2	no	—
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₅×#335	C₂²	1	2	yes	—
38	C₅×#334	C₂²	1	2	yes	—
39	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×D₄⋊C₈	C₂²	1	2	yes	—
42	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×D₄⋊C₈	C₂²	1	2	yes	—
44	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×#322	C₂²	1	2	yes	—
46	C₅×#322	C₂²	1	2	yes	—
47	#18025	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	1	no	—
49	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
52	C₂×C₅×M₁₆	—	2	1	no	—
53	C₂×C₅×M₁₆	—	2	2	no	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂²×C₅×C₈	—	2	1	no	—
56	C₂²×C₅×C₈	—	2	2	no	—
57	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₅×#127	C₂×C₄	1	1	yes	characteristic
59	C₅×#124	—	2	1	no	—
60	C₅×#121	—	2	1	no	—
61	C₅×#121	C₂×C₄	1	2	yes	—
62	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	—	2	1	no	—
66	C₄×C₅×D₄	—	2	1	no	—
67	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
68	C₄×C₅×D₄	C₂³	1	2	yes	—
69	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
70	C₅×#117	—	2	1	no	—
71	C₅×#117	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#107	C₂×C₄	1	2	yes	—
75	C₅×#106	C₂×C₄	1	2	yes	—
76	C₅×C₄⋊C₈	—	2	2	no	—
77	C₅×C₄⋊C₈	—	2	1	no	—
78	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
81	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₅×C₄⋊C₈	C₂³	1	2	yes	—
83	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×#103	C₂×C₄	1	2	yes	—
86	C₅×#102	C₂×C₄	1	2	yes	—
87	C₅×#102	C₂×C₄	1	2	yes	—
88	C₅×#102	C₂×C₄	1	2	yes	—
89	C₅×C₂²⋊C₈	—	2	1	no	—
90	C₅×C₂²⋊C₈	—	2	2	no	—
91	C₅×C₂²⋊C₈	—	2	2	no	—
92	C₅×C₂²⋊C₈	—	2	2	no	—
93	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₅×C₂²⋊C₈	D₄	1	2	yes	—
95	C₄×C₅×C₈	—	2	2	no	—
96	C₄×C₅×C₈	—	2	1	no	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×C₈	C₂³	1	2	yes	—
101	C₄×C₅×C₈	C₂³	1	2	yes	—
102	#3106	C₂×C₅	1	1	yes	characteristic
103	#2991	C₂×C₅	1	1	yes	characteristic, complemented
104	#2979	C₂×C₅	1	1	yes	characteristic, complemented
105	#1594	C₂×C₅	1	2	yes	complemented
106	#1583	C₂×C₅	1	2	yes	complemented
107	#1581	C₂×C₅	1	2	yes	complemented
108	SD₁₆⋊C₈	C₂×C₅	1	2	yes	complemented
109	#1574	C₂×C₅	1	1	yes	characteristic, complemented
110	#1492	C₂×C₅	1	1	yes	characteristic, complemented
111	#1476	C₂×C₅	1	1	yes	characteristic, complemented
112	#1452	C₂×C₅	1	1	yes	characteristic, complemented
113	C₅×#41	—	2	2	no	—
114	C₅×#41	—	4	1	no	—
115	C₅×#41	—	8	1	no	—
116	C₅×#41	—	8	1	no	—
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	2	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×SD₁₆	—	2	4	no	—
133	C₅×D₈	—	4	2	no	—
134	C₅×M₁₆	—	8	2	no	—
135	C₅×M₁₆	—	8	2	no	—
136	C₅×M₁₆	—	8	1	no	—
137	C₂×C₅×C₈	—	2	1	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	—	2	1	no	—
142	C₂×C₅×C₈	—	4	2	no	—
143	C₂×C₅×C₈	—	8	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	2	yes	—
147	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	2	2	no	—
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₅×C₂²⋊C₄	—	2	2	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₅	#41	1	1	yes	characteristic
165	C₄²×C₅	C₂⁴	1	1	yes	characteristic
166	#532	C₂²×C₅	1	1	yes	characteristic
167	C₄×#41	C₂²×C₅	1	1	yes	characteristic
168	#482	C₄×C₅	1	2	yes	—
169	#477	C₄×C₅	1	1	yes	characteristic
170	#476	C₄×C₅	1	1	yes	characteristic
171	#460	C₄×C₅	1	1	yes	characteristic
172	#459	C₄×C₅	1	1	yes	characteristic
173	#449	C₄×C₅	1	2	yes	—
174	C₈×Q₈	C₂²×C₅	1	2	yes	—
175	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
176	C₄×D₈	C₂²×C₅	1	2	yes	—
177	#436	—	2	1	no	—
178	#436	—	2	2	no	—
179	#436	C₂²×C₅	1	2	yes	—
180	#436	C₂²×C₅	1	2	yes	—
181	C₈×D₄	—	2	1	no	—
182	C₈×D₄	C₂²×C₅	1	2	yes	—
183	#431	—	2	1	no	—
184	#431	C₂²×C₅	1	1	yes	characteristic
185	#431	C₂²×C₅	1	1	yes	characteristic
186	#431	C₂²×C₅	1	1	yes	characteristic
187	#423	—	2	1	no	—
188	#423	C₂²×C₅	1	1	yes	characteristic
189	#408	—	2	2	no	—
190	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
191	#335	C₂²×C₅	1	2	yes	—
192	#334	C₂²×C₅	1	2	yes	—
193	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
194	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
195	D₄⋊C₈	C₂²×C₅	1	2	yes	—
196	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
197	D₄⋊C₈	C₂²×C₅	1	2	yes	—
198	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
199	#322	C₂²×C₅	1	2	yes	—
200	#322	C₂²×C₅	1	2	yes	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	2	no	—
203	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
204	C₅×Q₈	—	2	1	no	—
205	C₅×Q₈	—	8	1	no	—
206	C₅×Q₈	#131	1	2	yes	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	2	1	no	—
209	C₅×D₄	—	2	1	no	—
210	C₅×D₄	—	2	2	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	—	4	2	no	—
213	C₅×D₄	—	8	1	no	—
214	C₅×D₄	—	8	2	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	4	2	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	2	no	—
237	C₅×C₈	—	2	2	no	—
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	2	2	no	—
240	C₅×C₈	—	4	1	no	—
241	C₅×C₈	—	4	1	no	—
242	C₅×C₈	—	4	1	no	—
243	C₅×C₈	—	4	2	no	—
244	C₅×C₈	—	4	1	no	—
245	C₂×#41	—	2	1	no	—
246	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
247	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
248	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
255	#127	C₂×C₄×C₅	1	1	yes	characteristic
256	#124	—	2	1	no	—
257	#121	—	2	1	no	—
258	#121	C₂×C₄×C₅	1	2	yes	—
259	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
260	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
265	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
266	C₄×D₄	C₂³×C₅	1	2	yes	—
267	#117	—	2	1	no	—
268	#117	C₂×C₄×C₅	1	1	yes	characteristic
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
271	#107	C₂×C₄×C₅	1	2	yes	—
272	#106	C₂×C₄×C₅	1	2	yes	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
276	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
277	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
278	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
279	C₄⋊C₈	C₂³×C₅	1	2	yes	—
280	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
281	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
282	#103	C₂×C₄×C₅	1	2	yes	—
283	#102	C₂×C₄×C₅	1	2	yes	—
284	#102	C₂×C₄×C₅	1	2	yes	—
285	#102	C₂×C₄×C₅	1	2	yes	—
286	C₂²⋊C₈	—	2	1	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₂²⋊C₈	—	2	2	no	—
290	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
291	C₂²⋊C₈	C₅×D₄	1	2	yes	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
296	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₅	1	2	yes	—
298	C₄×C₈	C₂³×C₅	1	2	yes	—
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	4	1	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	—	4	2	no	—
305	C₂²×C₅	—	4	1	no	—
306	C₂²×C₅	—	4	1	no	—
307	C₂²×C₅	—	4	2	no	—
308	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	2	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	4	1	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	4	1	no	—
316	C₄×C₅	#444	1	2	yes	—
317	C₄×C₅	C₂×#131	1	1	yes	characteristic
318	C₄×C₅	#568	1	1	yes	characteristic
319	C₄×C₅	#576	1	1	yes	characteristic
320	C₄×C₅	#577	1	1	yes	characteristic
321	#41	—	2	2	no	—
322	#41	—	4	1	no	—
323	#41	—	8	1	no	—
324	#41	—	8	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
332	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₅×#41	1	1	yes	characteristic
340	SD₁₆	—	2	4	no	—
341	D₈	—	4	2	no	—
342	M₁₆	—	8	2	no	—
343	M₁₆	—	8	2	no	—
344	M₁₆	—	8	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	8	2	no	—
352	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
353	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
354	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
355	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
361	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
371	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
372	C₄²	C₅×#41	1	1	yes	characteristic
373	C₄²	C₂⁴×C₅	1	1	yes	characteristic
374	C₂×C₅	—	4	1	no	—
375	C₂×C₅	—	8	1	no	—
376	C₂×C₅	—	8	2	no	—
377	C₂×C₅	#2933	1	1	yes	characteristic
378	C₂×C₅	#2946	1	1	yes	characteristic
379	C₂×C₅	C₂×#444	1	1	yes	characteristic
380	C₂³	—	2	1	no	—
381	C₂³	—	2	2	no	—
382	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	8	1	no	—
385	Q₈	C₅×#131	1	2	yes	—
386	D₄	—	2	2	no	—
387	D₄	—	2	1	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
410	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
411	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
414	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	1	no	—
424	C₅	#18025	1	1	yes	characteristic, direct product factor, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	C₅×#444	1	2	yes	—
443	C₄	C₂×C₅×#131	1	1	yes	characteristic
444	C₄	C₅×#568	1	1	yes	characteristic
445	C₄	C₅×#576	1	1	yes	characteristic
446	C₄	C₅×#577	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	—	8	2	no	—
450	C₂	C₅×#2933	1	1	yes	characteristic
451	C₂	C₅×#2946	1	1	yes	characteristic
452	C₂	C₂×C₅×#444	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×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2991	C₂	semidirect
3. C₅×#2979	C₂	semidirect
4. C₅×#1594	C₂	semidirect
5. C₅×#1583	C₂	semidirect
6. C₅×#1581	C₂	semidirect
7. C₅×SD₁₆⋊C₈	C₂	semidirect
8. C₅×#1574	C₂	semidirect
9. C₅×#1492	C₂	semidirect
10. C₅×#1476	C₂	semidirect
11. C₅×#1452	C₂	semidirect
47. #18025	C₅	direct (N × H)
103. #2991	C₂×C₅	semidirect
104. #2979	C₂×C₅	semidirect
105. #1594	C₂×C₅	semidirect
106. #1583	C₂×C₅	semidirect
107. #1581	C₂×C₅	semidirect
108. SD₁₆⋊C₈	C₂×C₅	semidirect
109. #1574	C₂×C₅	semidirect
110. #1492	C₂×C₅	semidirect
111. #1476	C₂×C₅	semidirect
112. #1452	C₂×C₅	semidirect
424. C₅	#18025	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×#3106	2
C₅×#2991	2
C₅×#2979	2
C₅×#1594	2
C₅×#1583	2
C₅×#1581	2
C₅×SD₁₆⋊C₈	2
C₅×#1574	2
C₅×#1492	2
C₅×#1476	2
C₅×#1452	2
#18025	5

Subgroups — C5×#18025 #11940745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18025 #11940745