Subgroups — C₅×#22230 #11944950

Order 1280.

846 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic
2	C₅×#2331	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2328	C₂	1	1	yes	maximal, characteristic
4	C₅×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1961	C₂	1	1	yes	maximal, characteristic
6	C₅×#1926	C₂	1	2	yes	maximal, complemented
7	C₅×#1925	C₂	1	2	yes	maximal, complemented
8	C₅×#1864	C₂	1	2	yes	maximal, complemented
9	C₅×#1862	C₂	1	2	yes	maximal, complemented
10	C₅×#1846	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
15	C₅×#486	C₄	1	8	yes	complemented
16	C₂×C₅×#107	C₂²	1	2	yes	—
17	C₂×C₅×#106	C₂²	1	2	yes	—
18	C₂×C₅×#102	C₂²	1	2	yes	—
19	C₂×C₅×#102	C₂²	1	2	yes	—
20	C₂×C₅×#102	C₂²	1	2	yes	—
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₂×C₅×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₅×#391	—	2	2	no	—
25	C₅×#390	C₂²	1	2	yes	—
26	C₅×#389	C₂²	1	2	yes	—
27	C₅×#387	—	2	2	no	—
28	C₅×#386	—	2	2	no	—
29	C₅×#386	—	2	2	no	—
30	C₅×#382	C₂²	1	1	yes	characteristic
31	C₅×#382	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
33	C₅×#376	C₂²	1	1	yes	characteristic
34	C₅×#340	C₂²	1	2	yes	—
35	C₅×#340	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	1	yes	characteristic
37	C₅×#336	C₂²	1	1	yes	characteristic
38	C₅×#336	C₂²	1	1	yes	characteristic
39	C₅×#336	C₂²	1	1	yes	characteristic
40	#22230	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₅×Q₈	—	2	1	no	—
42	C₂²×C₅×D₄	—	2	1	no	—
43	C₂²×C₅×D₄	—	2	1	no	—
44	C₂²×C₅×D₄	C₂³	1	2	yes	—
45	C₂³×C₄×C₅	—	2	2	no	—
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₅×C₄⋊Q₈	—	2	2	no	—
51	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
52	C₅×#127	—	2	2	no	—
53	C₅×#127	C₂×C₄	1	4	yes	—
54	C₄×C₅×D₄	—	4	2	no	—
55	C₄×C₅×D₄	—	4	2	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₅	—	2	2	no	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×#107	—	4	2	no	—
69	C₅×#106	—	4	2	no	—
70	C₅×#102	—	4	2	no	—
71	C₅×#102	—	4	2	no	—
72	C₅×#102	C₂×C₄	1	8	yes	complemented
73	C₅×#102	C₂×C₄	1	8	yes	complemented
74	C₅×#97	—	2	2	no	—
75	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
76	C₅×#95	—	2	2	no	—
77	C₅×#95	—	2	1	no	—
78	C₅×#95	—	2	1	no	—
79	C₅×#95	—	2	1	no	—
80	C₅×#95	—	2	1	no	—
81	C₅×#95	—	2	2	no	—
82	C₅×#95	D₄	1	2	yes	—
83	C₅×#95	D₄	1	2	yes	—
84	C₂×#486	C₂×C₅	1	1	yes	characteristic
85	#2331	C₂×C₅	1	1	yes	characteristic, complemented
86	#2328	C₂×C₅	1	1	yes	characteristic
87	#1993	C₂×C₅	1	1	yes	characteristic, complemented
88	#1961	C₂×C₅	1	1	yes	characteristic
89	#1926	C₂×C₅	1	2	yes	complemented
90	#1925	C₂×C₅	1	2	yes	complemented
91	#1864	C₂×C₅	1	2	yes	complemented
92	#1862	C₂×C₅	1	2	yes	complemented
93	#1846	C₂×C₅	1	1	yes	characteristic, complemented
94	#1746	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂⁴×C₅	—	2	2	no	—
96	C₂×C₅×Q₈	—	2	4	no	—
97	C₂×C₅×Q₈	—	8	2	no	—
98	C₂×C₅×D₄	—	2	4	no	—
99	C₂×C₅×D₄	—	2	4	no	—
100	C₂×C₅×D₄	—	2	2	no	—
101	C₂×C₅×D₄	—	2	2	no	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	8	2	no	—
106	C₂×C₅×D₄	—	8	2	no	—
107	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	4	4	no	—
112	C₂²×C₄×C₅	—	8	2	no	—
113	C₂²×C₄×C₅	—	8	2	no	—
114	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₂×C₅×C₈	—	2	1	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
131	C₅×C₄⋊C₄	—	2	4	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	8	2	no	—
138	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
139	C₅×C₂²⋊C₄	—	4	4	no	—
140	C₅×C₂²⋊C₄	—	8	2	no	—
141	C₅×C₂²⋊C₄	—	8	2	no	—
142	C₄²×C₅	—	2	1	no	—
143	C₄²×C₅	—	2	1	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	—	8	2	no	—
147	C₄²×C₅	C₂²×C₄	1	2	yes	—
148	C₄²×C₅	#41	1	2	yes	—
149	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
150	C₂×#127	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
152	#486	C₄×C₅	1	8	yes	complemented
153	C₂×#107	C₂²×C₅	1	2	yes	—
154	C₂×#106	C₂²×C₅	1	2	yes	—
155	C₂×#102	C₂²×C₅	1	2	yes	—
156	C₂×#102	C₂²×C₅	1	2	yes	—
157	C₂×#102	C₂²×C₅	1	2	yes	—
158	C₂×#102	C₂²×C₅	1	2	yes	—
159	C₂×#97	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
161	#391	—	2	2	no	—
162	#390	C₂²×C₅	1	2	yes	—
163	#389	C₂²×C₅	1	2	yes	—
164	#387	—	2	2	no	—
165	#386	—	2	2	no	—
166	#386	—	2	2	no	—
167	#382	C₂²×C₅	1	1	yes	characteristic
168	#382	C₂²×C₅	1	1	yes	characteristic
169	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
170	#376	C₂²×C₅	1	1	yes	characteristic
171	#340	C₂²×C₅	1	2	yes	—
172	#340	C₂²×C₅	1	2	yes	—
173	#336	C₂²×C₅	1	1	yes	characteristic
174	#336	C₂²×C₅	1	1	yes	characteristic
175	#336	C₂²×C₅	1	1	yes	characteristic
176	#336	C₂²×C₅	1	1	yes	characteristic
177	C₂³×C₅	—	2	4	no	—
178	C₂³×C₅	—	4	2	no	—
179	C₂³×C₅	—	4	2	no	—
180	C₂³×C₅	—	4	2	no	—
181	C₂³×C₅	—	4	2	no	—
182	C₂³×C₅	—	4	2	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₅×Q₈	—	8	4	no	—
186	C₅×D₄	—	2	4	no	—
187	C₅×D₄	—	2	4	no	—
188	C₅×D₄	—	4	2	no	—
189	C₅×D₄	—	4	2	no	—
190	C₅×D₄	—	8	4	no	—
191	C₅×D₄	—	8	4	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	4	no	—
195	C₂×C₄×C₅	—	2	2	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	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	8	8	no	—
210	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
212	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
218	C₅×C₈	—	2	2	no	—
219	C₅×C₈	—	2	2	no	—
220	C₅×C₈	—	4	1	no	—
221	C₅×C₈	—	4	1	no	—
222	C₂²×Q₈	—	2	1	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	C₂³×C₅	1	2	yes	—
226	C₂³×C₄	—	2	2	no	—
227	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
233	#127	—	2	2	no	—
234	#127	C₂×C₄×C₅	1	4	yes	—
235	C₄×D₄	—	4	2	no	—
236	C₄×D₄	—	4	2	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
249	#107	—	4	2	no	—
250	#106	—	4	2	no	—
251	#102	—	4	2	no	—
252	#102	—	4	2	no	—
253	#102	C₂×C₄×C₅	1	8	yes	complemented
254	#102	C₂×C₄×C₅	1	8	yes	complemented
255	#97	—	2	2	no	—
256	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
257	#95	—	2	2	no	—
258	#95	—	2	1	no	—
259	#95	—	2	1	no	—
260	#95	—	2	1	no	—
261	#95	—	2	1	no	—
262	#95	—	2	2	no	—
263	#95	C₅×D₄	1	2	yes	—
264	#95	C₅×D₄	1	2	yes	—
265	C₂²×C₅	—	4	4	no	—
266	C₂²×C₅	—	4	4	no	—
267	C₂²×C₅	—	4	4	no	—
268	C₂²×C₅	—	8	2	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	—	8	2	no	—
271	C₂²×C₅	—	8	2	no	—
272	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₅	#535	1	1	yes	characteristic
274	C₂²×C₅	#536	1	1	yes	characteristic
275	C₂²×C₅	#576	1	2	yes	—
276	C₂²×C₅	#577	1	2	yes	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	2	2	no	—
279	C₄×C₅	—	4	4	no	—
280	C₄×C₅	—	4	2	no	—
281	C₄×C₅	—	4	2	no	—
282	C₄×C₅	—	8	2	no	—
283	C₄×C₅	—	8	2	no	—
284	C₄×C₅	#520	1	1	yes	characteristic
285	C₄×C₅	#520	1	1	yes	characteristic
286	C₄×C₅	#542	1	1	yes	characteristic
287	C₄×C₅	#542	1	1	yes	characteristic
288	C₂⁴	—	2	2	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	8	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	8	2	no	—
299	C₂×D₄	—	8	2	no	—
300	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	8	2	no	—
306	C₂²×C₄	—	8	2	no	—
307	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
308	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
309	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
323	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	8	2	no	—
331	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	8	2	no	—
334	C₂²⋊C₄	—	8	2	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	8	2	no	—
340	C₄²	C₂²×C₄×C₅	1	2	yes	—
341	C₄²	C₅×#41	1	2	yes	—
342	C₂×C₅	—	8	4	no	—
343	C₂×C₅	#2326	1	1	yes	characteristic
344	C₂×C₅	#2948	1	1	yes	characteristic
345	C₂×C₅	#2949	1	1	yes	characteristic
346	C₂×C₅	#3224	1	2	yes	—
347	C₂×C₅	#3241	1	2	yes	—
348	C₂³	—	2	4	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
356	Q₈	—	8	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	4	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	8	4	no	—
362	D₄	—	8	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	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	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	8	8	no	—
381	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
382	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
383	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
384	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
385	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
386	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
388	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₅	#22230	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
402	C₂²	C₅×#535	1	1	yes	characteristic
403	C₂²	C₅×#536	1	1	yes	characteristic
404	C₂²	C₅×#576	1	2	yes	—
405	C₂²	C₅×#577	1	2	yes	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	2	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	2	no	—
413	C₄	C₅×#520	1	1	yes	characteristic
414	C₄	C₅×#520	1	1	yes	characteristic
415	C₄	C₅×#542	1	1	yes	characteristic
416	C₄	C₅×#542	1	1	yes	characteristic
417	C₂	—	8	4	no	—
418	C₂	C₅×#2326	1	1	yes	characteristic
419	C₂	C₅×#2948	1	1	yes	characteristic
420	C₂	C₅×#2949	1	1	yes	characteristic
421	C₂	C₅×#3224	1	2	yes	—
422	C₂	C₅×#3241	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	C₂×C₅×#127	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. C₅×#2331	C₂	semidirect
4. C₅×#1993	C₂	semidirect
6. C₅×#1926	C₂	semidirect
7. C₅×#1925	C₂	semidirect
8. C₅×#1864	C₂	semidirect
9. C₅×#1862	C₂	semidirect
10. C₅×#1846	C₂	semidirect
11. C₅×#1746	C₂	semidirect
15. C₅×#486	C₄	semidirect
40. #22230	C₅	direct (N × H)
51. C₅×C₄⋊Q₈	C₂×C₄	semidirect
72. C₅×#102	C₂×C₄	semidirect
73. C₅×#102	C₂×C₄	semidirect
75. C₄×C₅×C₈	C₂×C₄	semidirect
85. #2331	C₂×C₅	semidirect
87. #1993	C₂×C₅	semidirect
89. #1926	C₂×C₅	semidirect
90. #1925	C₂×C₅	semidirect
91. #1864	C₂×C₅	semidirect
92. #1862	C₂×C₅	semidirect
93. #1846	C₂×C₅	semidirect
94. #1746	C₂×C₅	semidirect
152. #486	C₄×C₅	semidirect
232. C₄⋊Q₈	C₂×C₄×C₅	semidirect
253. #102	C₂×C₄×C₅	semidirect
254. #102	C₂×C₄×C₅	semidirect
256. C₄×C₈	C₂×C₄×C₅	semidirect
393. C₅	#22230	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×#486	2
C₅×#2331	2
C₅×#2328	2
C₅×#1993	2
C₅×#1961	2
C₅×#1926	2
C₅×#1925	2
C₅×#1864	2
C₅×#1862	2
C₅×#1846	2
C₅×#1746	2
#22230	5

Subgroups — C5×#22230 #11944950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22230 #11944950