Subgroups — C₅×#29848 #11952568

Order 1280.

740 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#433	C₂	1	1	yes	maximal, characteristic
3	C₅×#2628	C₂	1	1	yes	maximal, characteristic
4	C₅×#2621	C₂	1	1	yes	maximal, characteristic
5	C₅×#2068	C₂	1	2	yes	maximal, complemented
6	C₅×#2066	C₂	1	2	yes	maximal, complemented
7	C₅×#2036	C₂	1	2	yes	maximal
8	C₅×#2035	C₂	1	2	yes	maximal
9	C₅×#1993	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1960	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1846	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₅×#487	—	2	4	no	—
17	C₅×#433	—	2	4	no	—
18	C₂×C₅×#107	C₂²	1	2	yes	—
19	C₂×C₅×#106	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×#103	C₂²	1	2	yes	—
23	C₂×C₅×#103	C₂²	1	2	yes	—
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₅×#400	—	2	1	no	—
31	C₅×#399	—	2	1	no	—
32	C₅×#398	—	2	1	no	—
33	C₅×#398	—	2	1	no	—
34	C₅×#397	—	2	1	no	—
35	C₅×#397	—	2	1	no	—
36	C₅×#395	—	2	1	no	—
37	C₅×#393	—	2	1	no	—
38	C₅×#391	C₂²	1	2	yes	—
39	C₅×#389	C₂²	1	2	yes	—
40	C₅×#382	C₂²	1	1	yes	characteristic
41	C₅×#382	C₂²	1	1	yes	characteristic
42	C₅×#380	C₂²	1	2	yes	—
43	C₅×#340	C₂²	1	2	yes	—
44	C₅×#340	C₂²	1	2	yes	—
45	#29848	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₅×Q₈	—	2	1	no	—
47	C₂²×C₅×Q₈	C₂³	1	2	yes	—
48	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₅×C₄⋊Q₈	—	2	2	no	—
54	C₅×C₄⋊Q₈	—	2	2	no	—
55	C₅×C₄⋊Q₈	—	2	2	no	—
56	C₅×C₄⋊Q₈	—	2	2	no	—
57	C₅×C₂²⋊Q₈	—	4	2	no	—
58	C₅×C₂²⋊Q₈	—	4	2	no	—
59	C₅×#117	—	2	2	no	—
60	C₅×#117	—	2	2	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	—	2	2	no	—
66	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	—	4	2	no	—
78	C₅×#106	—	4	2	no	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×#103	—	2	4	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	—	4	2	no	—
84	C₅×#103	—	4	2	no	—
85	C₅×C₂²⋊C₈	—	2	2	no	—
86	C₅×C₂²⋊C₈	—	2	2	no	—
87	C₅×#97	—	2	2	no	—
88	C₄×C₅×C₈	D₄	1	4	yes	—
89	C₅×#95	—	2	2	no	—
90	C₅×#95	—	2	1	no	—
91	C₅×#95	—	2	1	no	—
92	C₅×#95	—	2	1	no	—
93	C₅×#95	—	2	1	no	—
94	C₅×#95	—	2	2	no	—
95	C₅×#95	—	2	2	no	—
96	C₅×#95	—	2	2	no	—
97	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂×#433	C₂×C₅	1	1	yes	characteristic
99	#2628	C₂×C₅	1	1	yes	characteristic
100	#2621	C₂×C₅	1	1	yes	characteristic
101	#2068	C₂×C₅	1	2	yes	complemented
102	#2066	C₂×C₅	1	2	yes	complemented
103	#2036	C₂×C₅	1	2	yes	—
104	#2035	C₂×C₅	1	2	yes	—
105	#1993	C₂×C₅	1	1	yes	characteristic, complemented
106	#1960	C₂×C₅	1	1	yes	characteristic, complemented
107	#1846	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	2	no	—
115	C₂×C₅×Q₈	—	4	2	no	—
116	C₂×C₅×Q₈	—	8	2	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
144	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	4	4	no	—
154	C₅×C₄⋊C₄	—	4	2	no	—
155	C₅×C₄⋊C₄	—	4	2	no	—
156	C₅×C₄⋊C₄	—	4	2	no	—
157	C₅×C₄⋊C₄	—	8	2	no	—
158	C₅×C₂²⋊C₄	—	2	2	no	—
159	C₅×C₂²⋊C₄	—	2	2	no	—
160	C₅×C₂²⋊C₄	—	4	4	no	—
161	C₅×C₂²⋊C₄	—	8	2	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₄²×C₅	C₂×D₄	1	2	yes	—
165	C₄²×C₅	#41	1	2	yes	—
166	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
169	C₂×#117	C₂²×C₅	1	1	yes	characteristic
170	#487	—	2	4	no	—
171	#433	—	2	4	no	—
172	C₂×#107	C₂²×C₅	1	2	yes	—
173	C₂×#106	C₂²×C₅	1	2	yes	—
174	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
176	C₂×#103	C₂²×C₅	1	2	yes	—
177	C₂×#103	C₂²×C₅	1	2	yes	—
178	C₂×#103	C₂²×C₅	1	2	yes	—
179	C₂×#103	C₂²×C₅	1	2	yes	—
180	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
182	C₂×#97	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
184	#400	—	2	1	no	—
185	#399	—	2	1	no	—
186	#398	—	2	1	no	—
187	#398	—	2	1	no	—
188	#397	—	2	1	no	—
189	#397	—	2	1	no	—
190	#395	—	2	1	no	—
191	#393	—	2	1	no	—
192	#391	C₂²×C₅	1	2	yes	—
193	#389	C₂²×C₅	1	2	yes	—
194	#382	C₂²×C₅	1	1	yes	characteristic
195	#382	C₂²×C₅	1	1	yes	characteristic
196	#380	C₂²×C₅	1	2	yes	—
197	#340	C₂²×C₅	1	2	yes	—
198	#340	C₂²×C₅	1	2	yes	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	2	no	—
203	C₂³×C₅	—	2	2	no	—
204	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₅×Q₈	—	4	2	no	—
206	C₅×Q₈	—	4	2	no	—
207	C₅×Q₈	—	4	2	no	—
208	C₅×Q₈	—	4	2	no	—
209	C₅×Q₈	—	8	4	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	4	2	no	—
232	C₂×C₄×C₅	—	4	2	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	#121	1	2	yes	—
236	C₂×C₄×C₅	#121	1	2	yes	—
237	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
242	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
243	C₅×C₈	—	2	2	no	—
244	C₅×C₈	—	2	2	no	—
245	C₅×C₈	—	4	1	no	—
246	C₅×C₈	—	4	1	no	—
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×Q₈	C₂³×C₅	1	2	yes	—
249	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	—	2	2	no	—
258	C₂²⋊Q₈	—	4	2	no	—
259	C₂²⋊Q₈	—	4	2	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
278	#107	—	4	2	no	—
279	#106	—	4	2	no	—
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	2	2	no	—
282	#103	—	2	4	no	—
283	#103	—	2	4	no	—
284	#103	—	4	2	no	—
285	#103	—	4	2	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	#97	—	2	2	no	—
289	C₄×C₈	C₅×D₄	1	4	yes	—
290	#95	—	2	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	—	2	1	no	—
294	#95	—	2	1	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	C₂²×C₅	—	4	1	no	—
299	C₂²×C₅	—	4	2	no	—
300	C₂²×C₅	—	4	2	no	—
301	C₂²×C₅	—	4	1	no	—
302	C₂²×C₅	—	4	1	no	—
303	C₂²×C₅	C₂×#121	1	1	yes	characteristic
304	C₂²×C₅	#535	1	1	yes	characteristic
305	C₂²×C₅	#536	1	1	yes	characteristic
306	C₂²×C₅	#577	1	2	yes	—
307	C₂²×C₅	#578	1	2	yes	—
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	—	4	1	no	—
311	C₄×C₅	—	4	1	no	—
312	C₄×C₅	—	4	1	no	—
313	C₄×C₅	—	8	2	no	—
314	C₄×C₅	—	8	2	no	—
315	C₄×C₅	—	8	2	no	—
316	C₄×C₅	—	8	2	no	—
317	C₄×C₅	#537	1	1	yes	characteristic
318	C₄×C₅	#537	1	1	yes	characteristic
319	C₄×C₅	#542	1	1	yes	characteristic
320	C₄×C₅	#542	1	1	yes	characteristic
321	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	8	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
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	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
357	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	8	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	8	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×C₅×D₄	1	2	yes	—
378	C₄²	C₅×#41	1	2	yes	—
379	C₂×C₅	—	8	1	no	—
380	C₂×C₅	#2620	1	1	yes	characteristic
381	C₂×C₅	#3057	1	1	yes	characteristic
382	C₂×C₅	#3059	1	1	yes	characteristic
383	C₂×C₅	#3225	1	2	yes	—
384	C₂×C₅	#3242	1	2	yes	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	8	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	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	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	C₅×#121	1	2	yes	—
422	C₂×C₄	C₅×#121	1	2	yes	—
423	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
424	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
425	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
428	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	2	2	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	1	no	—
433	C₅	#29848	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	C₂×C₅×#121	1	1	yes	characteristic
440	C₂²	C₅×#535	1	1	yes	characteristic
441	C₂²	C₅×#536	1	1	yes	characteristic
442	C₂²	C₅×#577	1	2	yes	—
443	C₂²	C₅×#578	1	2	yes	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	C₅×#537	1	1	yes	characteristic
454	C₄	C₅×#537	1	1	yes	characteristic
455	C₄	C₅×#542	1	1	yes	characteristic
456	C₄	C₅×#542	1	1	yes	characteristic
457	C₂	—	8	1	no	—
458	C₂	C₅×#2620	1	1	yes	characteristic
459	C₂	C₅×#3057	1	1	yes	characteristic
460	C₂	C₅×#3059	1	1	yes	characteristic
461	C₂	C₅×#3225	1	2	yes	—
462	C₂	C₅×#3242	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#487	C₂	semidirect
5. C₅×#2068	C₂	semidirect
6. C₅×#2066	C₂	semidirect
9. C₅×#1993	C₂	semidirect
10. C₅×#1960	C₂	semidirect
11. C₅×#1846	C₂	semidirect
45. #29848	C₅	direct (N × H)
97. C₂×#487	C₂×C₅	semidirect
101. #2068	C₂×C₅	semidirect
102. #2066	C₂×C₅	semidirect
105. #1993	C₂×C₅	semidirect
106. #1960	C₂×C₅	semidirect
107. #1846	C₂×C₅	semidirect
433. C₅	#29848	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×#487	2
C₂×C₅×#433	2
C₅×#2628	2
C₅×#2621	2
C₅×#2068	2
C₅×#2066	2
C₅×#2036	2
C₅×#2035	2
C₅×#1993	2
C₅×#1960	2
C₅×#1846	2
#29848	5

Subgroups — C5×#29848 #11952568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29848 #11952568